When his cruise ship, the Cuban Queen, runs aground near Florida on its way to Havana, New York ocean liner magnate Walter McCracken (George Barbier (actor)) sends his vice-president, Jay Williams (John Payne (actor)), to the site to forestall any legal action. Jay gets the passengers to sign claim waivers in exchange for future passage on another McCracken ocean liner. One passenger, Macy's salesclerk Nan Spencer (Alice Faye), refuses to sign, because she has saved for years for the vacation and cannot take it at any other time. When Nan hints that she is aware of the captain's negligence in the accident, Jay accedes to her demand that the company ensure her an enjoyable vacation in Havana. Nan refuses to sign the waiver until after her vacation is completed, so McCracken orders Jay to accompany her, even though he is soon to be married to McCracken's snobbish daughter Terry. Upon reaching Havana, Nan is delighted with the scenery but bored with Jay, who is too stodgy to provide the romance she craves. When charming fortune hunter Monte Blanca (Cesar Romero) comes across Nan, he believes that she will be the solution to his gambling debts.