Tour operator Pullmantur said its ship Ocean Dream with 759 passengers and 400 crew members was denied permission to dock in Grenada and Barbados after informing authorities there that crew members had flu symptoms.
The company said it later received confirmation that three crew members tested positive for swine flu. Another 11 have symptoms.
None of the 14 is seriously ill, it said.
The sick crew have been isolated and no passengers have fallen ill, the company said in a statement.
But the nine-day cruise that began in Aruba off Venezuela's coast is over, and the company is now making arrangements to get the passengers back to their ports of origin, company spokeswoman Ana del Hoyo said.
Passenger Miriam Tonk-Croes of Aruba complained that crew members weren't communicating with them.
"This is frustrating," she told Aruba radio station Canal 90. "We want to go somewhere."
Tonk-Croes said the ship is anchored near Venezuela's Isla Margarita.
- AP