Levačić announced her success on Tuesday, her 27th birthday, on social networks after swimming for about 11 hours in high waves, with the ocean's temperature of around 16 degrees Celsius.
Because of the low temperature of the ocean water and strong currents, the Cook Strait is considered one of the biggest swimming challenges.
Of the Ocean's Seven challenges, Levačić previously swam the Catalina Channel in California, the English Channel in Europe, the Molokai Channel in Hawaii, the Tsugaru Channel in Japan, the Strait of Gibraltar between Europe and Africa, and the North Channel between Northern Ireland and Scotland.
The first person to complete the Ocean's Seven was Stephen Redmond from Ireland, who did it in 2012.