Palmotić was born in 1606 in Ragusa, the son of Juraj Palmotić and Ursula née Gradić. His parents belonged to the notable patrician families of Palmotić and Gradić, respectively. Through his mother, he was related to Ivan Gundulić. He had an older brother Džore and younger Ivan, who died young in his childhood.
Aged 18, he became a member of the Great Council in the Republic of Ragusa. He began to write while still young, writing in continuation of the tradition of Ivan Gundulić inspired by Ovid, Virgil, Tasso and Ariosto. Although influenced by the Latin literary tradition, Palmotić wrote in his native Croatian language, as well as translating libretti from Italian. He also translated the Christias di Girolamo Vida, the Christiade, an 'Illyrian' poem in 24 verses, that was posthumously published in Rome in 1670. Although his poetry was melodramatic and dealt primarily with mythological topics, his drama focused on contemporary Dubrovnik, particularly the life of the aristocracy. In one of his songs he demonstrates his knowledge of the Serbian epic poetry mentioning its heroes like: Lazar of Serbia, Miloš Obilić, Skanderbeg, Sekula, Mihajlo Svilojević, Vuk Grgurević and John Hunyadi. His nephew Stjepan Gradić, ambassador and Vatican librarian, wrote about his life, supplying precious material to future biographers. Alongside Vinko Pribojević and Juraj Križanić, he was an early pioneer of the ideas of Slavic unity.
Pavlimir, drama. Narratives connected with the founding of Dubrovnik inspired his Pavlimir. This is a sort of Ragusan "Aeneid," Pavlimir corresponding to Aeneas. He comes from abroad, founds the city of Dubrovnik, marries the beautiful Margareta, whom he discovers there, and becomes otac slovenskog naroda.
Captislava, drama. The main character is the daughter of the King of Captat. She is in love with the Hungarian prince, Gradimir, but the father wants her to marry a Serbian prince. A nymph helps her in this cabal, and she elopes with the Hungarian prince, while her sister marries the Serbian prince. Chief roles are played by ghosts and nymphs.
Bisernica, drama. It is virtually the continuation of the Captislava, and almost all important roles are played by vilenice and vilenici.
Danica, drama. A dramatized episode from Ariosto's "Orlando Furioso", transplanted and acclimatized to the Bosnian and Ragusan soil. Danica is the enslaved daughter of the Bosnian king, Ostoja. She was saved by the Ragusan knight Matijas, who later became the ban of Croatia. Some motifs of this play are akin to Shakespeare's comedy Much Ado About Nothing.
In addition to his four important dramas in which Palmotta celebrated the exploits of Slavic heroes, he wrote several imitations based on Latin and Italian sources. Thus the material for his Allina was taken from Ariosto, and for the Armida from Tasso. The mythological play Atalanta is based on Ovid's "Metamorphoses".