The comedy, directed by Frank Tashlin, sees Doris Day as Jennifer Nelson, the widowed daughter of a glass-bottom boat operator who sometimes pretends to be a mermaid to entertain guests. When not swimming around as a mermaid, however, Nelson works for NASA. She gets caught (literally, by a fishing hook) by Rod Taylor's Bruce Templeton.
This is when hijinks ensue. Turns out Templeton is her boss, and he has designs on her. Others, however, think she's a spy. There's also an artifical gravity machine.