Galinović started his professional career with Croatian First League side NK Osijek, where he was part of the first team from 1993 until 2002.

In 2002, he moved to another Croatian First League side, NK Kamen Ingrad, and spent two seasons with the club as their first-choice goalkeeper.

He was then the club's first-choice goalkeeper in the 2005–06 UEFA Champions League season and appeared in all of their six group matches before they exited the competition in the first round.

Galinović made his international debut for the Croatia national team on 13 June 1999 in a friendly match against Egypt at the Korea Cup tournament in Seoul.

He mostly served as the team's third-choice goalkeeper, behind Stipe Pletikosa and Vedran Runje, making no appearances during the qualifying campaign.