Zrinjevac got its name in 1866. Before its name was New Square. The park on this square was officially opened on June 14th 1873 at the place where people organized a cattle fair.
The city authorities made a decision to decorate the muddy and dirty place exactly on the 300th anniversary of the victory over the Turks. Anniversary was about the defense of the Siget. That was also an anniversary of the death of great Croatian hero Nikola Subic Zrinski.
The project for the renovation of the square was made in 1870 by the first modern Zagreb urbanist, Rupert Melkus. After reconstruction, he competed on the beauty contenst with the gorgeous square of Franjo Josip I. (later renamed to King Tomislav square).