When Navy shipmates Russell J. "Rusty" Gibbs, Gerald "Biff" Jones, Chips and Gateleg go on shore leave, ladykiller Rusty is challenged by his friends to take dowdy librarian Doris Kimbell to the Crow's Nest Cafe, a popular Navy hangout. Accepting the bet, Rusty is soon at the library trying to romance an unimpressed Doris. As a cover, Rusty checks out a book on algebra in which Doris' beau, Julian Everett, is unusually interested. The two men escort Doris home, where Rusty receives a chilly reception from Doris' aunt, Beulah Wayne, who disapproves of common sailors. Rusty lies to them, saying that he is a candidate for Annapolis, although actually he is too old, and Doris is impressed enough to go walking on the beach with him the next day. He makes another date with her, but Chips and Gateleg tell the family the truth about Rusty not really being an Annapolis candidate. When Rusty goes to pick up Doris, she gives him the cold shoulder, but he lies to her again, telling her that he is in Naval Intelligence. Doris believes him and goes with him to the Crow's Nest, where Chips, Gateleg and Biff are stunned by the transformation Rusty has worked on the now beautiful Doris. Rusty wins his bet and leaves the cafe with Doris, but not before Julian, who really is a spy, overhears that Rusty is in intelligence. The next day, Julian and his cohorts, Dr. Crowley and Lawson, discuss their fear that Rusty may have solved their secret code, which is contained in the algebra book he borrowed from Doris' library. Meanwhile, on board the ship, Rusty's commanding officer asks the Washington, D.C. branch of Naval Intelligence to investigate Rusty, after which a real intelligence officer searches Rusty's locker and finds the secret code. Rusty keeps a date with Doris, during which he tries to tell her the truth about himself and that he loves her, but when Biff tells her about the bet, she runs away. While Rusty is trying to make up with Doris, Naval officers search for him, as they now suspect him of being involved in a plot to murder an important foreign nobleman. Rusty is kidnapped by Lawson and taken to Crowley's office, where he is interrogated about the book. After learning nothing from Rusty, Julian kidnaps Doris and then her uncle Andrew. Crowley receives another code book and deciphers a telegram about the nobleman's arrival, then leaves with Lawson to assassinate him, after which Rusty uses a lamp to signal his ship's officers to protect the nobleman. Rusty frees himself, struggles with Julian and then goes to the airport with Doris, Andrew and his pals. At the airport, Crowley and Lawson are captured just as the nobleman's plane is landing. Later, Rusty is rewarded with a promotion to warrant officer, and receives Beulah and Andrew's approval of his upcoming marriage to Doris.