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At a Navy recruiting station, bumbling, allergy-plagued Melvin Jones meets Al Crowther, a handsome crooner and ladies' man.  Al is applying for the eleventh time because he likes the attention that women, like entertainer Hetty Button, his latest conquest, give him when they think he is about to ship out, but is sure his trick knee will prevent him from passing the Navy's physical exam.  To Melvin's and Al's surprise, the Navy passes them both and sends them to a training camp in San Diego, along with Petty Officer Lardoski, a bully whom Al and Melvin have already antagonized.

At camp, Melvin is terrified at having his blood drawn during the routine physical and runs into Red Cross nurse Hilda Jones's office to hide.  Unknown to Melvin, Hilda mans the local blood bank and assumes he has come to donate.  After Melvin gives blood to please Hilda, who is attractive to him because she wears little makeup, something to which he is violently allergic, he is forced back to the physical, but baffles the staff with his now-bloodless veins.

Later, the men are trained in ship procedures, and Melvin manages to sink his rowboat.  As punishment, Lardoski cancels all of the recruits' liberty, but when Al is asked to sing on a television show as a Navy representative, he agrees on condition that liberty be reinstated.  Lardoski gives in, and on his way into town, Melvin meets Hilda and invites her to watch Al perform.

At the television station, Al and Melvin end up singing together, and Melvin is cajoled into judging a kissing contest sponsored by the "Tempting Kiss" cosmetics company, the first prize of which is a trip to Honolulu.  Because of his allergies, Melvin cannot stand being near the eager, made-up participants and dashes out of the studio.  The women pursue him into another studio, where bathing suit models, including a girl Lardoski fancies, are strutting for the cameras.  Lardoski's girl kisses Melvin, to the consternation of Lardoski, who is watching the broadcast in a bar.  Melvin finally is cornered outside the television station and kisses Hilda to end the contest.

Despite being named the winner, Hilda is furious at Melvin for allowing dozens of women to kiss him, and storms away.  Barely able to breathe, Melvin is carted off to the base hospital, and during his recuperation, Al and the other recruits bet Lardoski that Melvin can procure a kiss from French movie star Corinne Calvet, who is performing in Honolulu, where they are being shipped.

After Melvin reluctantly agrees to try to win the bet, Al breaks the news that their ship is a submarine.  At sea, the claustrophic Melvin creates havoc in the cramped quarters and is assigned to swab the deck as punishment.  When the commander orders a routine dive, Melvin is left topside and has to climb the conning tower to keep from drowning before being rescued.  Upon docking in Honolulu, the recruits are given shore leave and scurry to the hotel nightclub where Corinne is singing.  There, Melvin runs into Hilda, who is still mad at him.

After the sailor-hating Corinne rejects Lardoski's advances, Melvin tries unsuccessfully to woo her at her table.  Melvin then gets into a confrontation with another sailor who makes a pass at Corinne, and the recreation supervisor decides to pair the two in a boxing match.  Before the fight, Al encourages the terrified Melvin to think like a real boxer, and when his opponent hears Melvin talking like a tough professional, he panics and asks his brother, Killer Jackson, to fill in.  To Melvin's horror, Jackson is a seasoned pro, but Melvin lands a couple of lucky punches and knocks him out.  Aware that Lardoski has ordered the shore patrol to apprehend him before he finds Corinne at a beach luau, Melvin sneaks out of the gym and disguises himself as a rickshaw driver.

Al, meanwhile, sings a romantic ballad at the luau, and when Corinne hears him, she starts to fall for him.  As Al is about to kiss Corinne, her secretary interrupts to reveal that the sailors have made a bet that one of them will kiss the star.  Assuming that Al is the sailor, Corinne leaves, disgusted.  Melvin then dresses up like a male hula dancer to elude Lardoski and the shore patrol, but is identified when his grass skirt falls off, revealing his sailor pants.  After a brief but frantic chase, Lardoski corners Melvin, but Corinne intercedes, believing the skinny sailor is an innocent boy.  Corinne kisses Melvin on the cheek, and Melvin declares that he has won the bet.  Vindicated, Al makes up with Corinne, while Hilda finally forgives Melvin.  When they return to the San Diego pier, however, Hetty is waiting and overhears Al giving Corinne his standard farewell line.  After Hetty angrily accuses Al of two-timing her, Al runs away and is joined by the devoted Melvin.