She tried again twice in 2011, but her efforts ended after an 11-hour asthma attack and jellyfish stings.
Last year, she abandoned an attempt about halfway through after severe jellyfish stings and a lightning storm put her in danger.
Nyad was a swimming sensation before these attempts. In the 1970s, she won multiple swimming marathons and was one of the first women to swim around the island of Manhattan.
Nyad said she was 8 years old when she first dreamed about swimming across the Straits of Florida. At the time, she was in Cuba on a trip from her home in Florida in the 1950s, before Fidel Castro led a Communist takeover in Cuba and the country's relations with the United States soured.
The Los Angeles woman had said this was going to be her final attempt.