Australian woman Penny Palfrey has fallen just short of reaching her goal of swimming unassisted from Cuba to Florida.

The mother of three and grandmother of two had been seeking to become the first to complete the historic feat without a protective shark cage.

"Penny Palfrey had to be pulled out of the water, after swimming for more [than] 40 hours," her team said in a tweet.

It said Palfrey had to abort her bid to reach the Florida Keys at about midnight on Sunday (local time) due to a strong southeast current "that made it impossible for her to continue her swim".

"Penny is presently on her escort boat being taken care of by her crew," the team said.

The 49-year-old, who left the Cuban capital of Havana on Friday morning (local time), had already covered 139 kilometres, or three-quarters of her itinerary when she ran into trouble.

She was just 43km south of Key West, her final destination.

By making it this far, she has already broken her own world record of the longest unassisted ocean swim of 110.45km, her team members said.

Despite her failure, her Facebook page quickly filled with comments by well-wishers, expressing support and saying that making it so far was already a great achievement.

"She is still the boss in the water. She is all business," her crew said in a Facebook post.

Palfrey faced many risks during her bid to complete the 166-kilometer trek to Key West.

Early this morning Palfrey reported seeing hammerhead sharks below her that "quickly vanished".

Palfrey's support team also reported that she had suffered "constant" jellyfish stings overnight and that her mouth was "very sore and painful".

Aside from sharks and jellyfish she also fought physical and mental fatigue, as well as fending off dehydration.

Her swim follows two unsuccessful attempts last year by American marathoner Diana Nyad, now 62, to cross the Florida Straits, which are known for tricky currents and unpredictable weather.

The swim was completed successfully by Australian swimmer Susan Maroney in May 1997, but unlike Nyad and Palfrey she used a shark cage.

Palfrey had been seeking to accomplish the feat in a "call for friendly relations between the peoples of the United States and Cuba," according to the Cuban foreign ministry.

Palfrey, who was born in Britain and moved to Australia at the age of 19, is among the most accomplished open-water swimmers in the world and has completed swims in the Caribbean and Pacific without a shark cage.

Two years ago, she crossed the Strait of Gibraltar between Spain and Morocco in three hours and three minutes, setting a new record for women.

Last year, Palfrey - who began swimming at age nine - swam from Little Cayman to Grand Cayman Island, again without a cage.