In December, the group's mission failed after its boat was damaged when it collided with an Israeli naval ship.
Free Gaza organisers accused the Israelis of ramming the boat, but Israeli officials said the collision occurred when the protesters' boat attempted to outmanoeuvre the Israeli vessel.
Earlier missions had successfully reached Gaza and, on each occasion, the Israeli authorities had been notified of the boat's movements.
Huwaida Arraf, an organiser, said: "I can't anticipate what the Israelis are going to do, but I know we won't be turned back easily.
"If they ram us again or use force against us, it will be nothing less than a premeditated attack against a defenseless boat.''
Arraf said organisers had been told that Israel sent a message to the authorities in Larnaca saying the boat would be turned back.
Sofia Sakorafa, deputy of the Greek Socialist party, said she was afraid but wanted to show solidarity with those who are suffering.
Ali Dabbagh, a Dubai-based eye surgeon on board the boat, said he planned to work in Gaza for four weeks.
"I'm not afraid," he said. "There's more fear of me looking back in the mirror and seeing someone who didn't do anything."
Israel imposed a blockade on Gaza in June 2007 as a means of isolating Hamas after it won Palestinian parliamentary elections.
Since then, there have been severe shortages of basic foodstuffs, fuel and medicines causing malnutrition among children and prompting aid groups to warn of a humanitarian crisis among the population of 1.5 million.
The closure of Gaza's crossings by the Israeli and Egyptian authorities has also meant that very few Gazans have been able to leave.