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In 1924, Red Nichols, a superb cornet player despite his naiveté, travels from his small hometown in Utah to New York City to join the band of crooner Wil Paradise.  Red irritates the smug Paradise by offering to play in the new, jazzier New Orleans style, and when Paradise angrily rebukes him, Red asserts that before long, all of his fellow musicians will be working for him.

Later, musician Tony Valani asks Red to join him on a double date with two chorus girls, Bobbie Meredith and Tommye Eden, but Red insists that they go to Harlem to hear Louis Armstrong, a black trumpet player from the South.  Tony acquiesces to Red’s demand and the quartet goes to the club, although Bobbie assumes that Red is a boring hick because he is from Utah.  At the club, which is actually a speakeasy, Red is awed by Louis’ talent while Bobbie, who correctly surmises that Red has never before imbibed, gets him drunk as a joke.  Bobbie regrets her actions, however, when Red, inspired by Louis, takes the stage to play with him and makes a fool of himself.

After the embarrassed Red sobers up, he reveals to Bobbie that his real name is Ernest Loring Nichols, and, contrite, she confesses that her name is Willa Stutsman and that she also is from a close family.  When Bobbie still does not believe that Red can really play, however, he accompanies Louis from the back of the club, and Louis and the audience are thrilled by Red’s skill.  Red gets Bobbie a job as a singer with Paradise’s band, and the couple soon marries.

On the evening of their wedding, Red is so irritated by Paradise’s hypocrisy that he quits and also costs Bobbie her job.  Bobbie cannot maintain her fury at Red, however, after he confesses that he pawned his treasured cornet to pay for their bridal suite.  Resigning herself that she will never know what her impulsive yet talented husband will do, Bobbie follows Red as he takes numerous radio jobs, which he invariably loses due to his clowning.

One day, Bobbie goes to their neighborhood deli and there joins a group of musicians, including Jimmy Dorsey, Glenn Miller, Artie Schutt and Dave Tough.  When they joke about Red’s impractical dreams, Bobbie berates them for not even reading his latest arrangements, and upon realizing that Bobbie is pregnant, the chastened musicians reconsider Red's arrangements.

Impressed, they join Red and soon, as Red Nichols and His Five Pennies, they are producing one hit record after another by playing Red’s Dixieland-style jazz.  Bobbie accompanies Red and the band on their nonstop tours, but after she has the baby, a girl they name Dorothy, Red decides to settle down.  Bobbie assures Red that the baby will not interfere with his career, and soon, Dorothy joins them on the road.

Five years pass as the band’s fame continues to spread during their travels, and Dorothy grows accustomed to their itinerant lifestyle.  One night, however, while Bobbie is away visiting her sister, Red takes Dorothy with him to listen to Louis, with whom he has become close friends.  When Bobbie suddenly returns home, she is appalled to find Dorothy at the late-night jam session, and tells Red that they must settle down for their daughter’s sake.  Red confesses that he wants to continue touring and persuades Bobbie to put Dorothy in a San Francisco boarding school, “just for a little while.” Dorothy is deeply resentful of Red’s decision, especially as her parents’ visits become more infrequent.

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Then one day, Red learns that Dorothy has fallen ill and when he rushes to join Bobbie at her side, is told that she has polio.  The sullen Dorothy refuses to acknowledge Red, who, heartbroken and believing that Dorothy’s illness is his fault, throws his cornet off the Golden Gate Bridge into the San Francisco Bay.  Determined to do everything he can to enable his daughter to walk again, Red quits the music business, buys a small house for his family in Los Angeles and takes a job at the nearby shipyards.

Red and Bobbie work hard on Dorothy’s physical therapy, and by her fourteenth birthday, she is able to walk with the use of canes.  At her birthday party, her friends laugh at the idea that her father was once a famous musician, which Dorothy herself can barely remember.  They play some of his old records, however, and are impressed.

Meanwhile, Red is at the shipyard where Glenn, now the leader of his own successful band, is performing to encourage the workers in their wartime efforts.  Tiredly telling a co-worker that he has heard the music before, Red leaves before the concert ends and joins Dorothy’s party.  Red is angered by the teenagers’ condescending attitude toward his musical career, but when he tries to demonstrate that he really can play, only a few sour notes issue from an old cornet that Tony had sent to Bobbie in case Red ever wanted it.

Declaring that he has lost his ability to play, Red spurns Tony’s offer to help him get a club date when Bobbie arranges for them to meet.  Dorothy, realizing that her father gave up music for her, urges Red not to be a quitter, just as he used to encourage her to regain her strength.  Still unsure of himself, Red is reluctant, but with his wife and daughter behind him, he begins to practice.

Two months later, Tony gets Red a “gig” in a small nightclub and on opening night, Red is deeply disappointed that none of his old friends have come to see him.  Although only Dorothy, Bobbie and a few disinterested drinkers are in the club, Red begins the show.  As he plays, he is astonished to hear Louis, Glenn and all his old band mates parade in, playing along with him.  A huge audience also pours into the club, and Red gleefully jams with Louis.  After their triumphant number, Red asks Bobbie to join him on stage, and she tells him that she has a surprise for him.  Dorothy then walks to the center of the dance floor without the aid of her cane and, curtsying to her father, asks him for a dance.  Overwhelmed, Red sweeps his daughter up to the stage and joins his friends in another number.