Born in Mostar, Grgić went through the ranks of Čitluk's NK Brotnjo before moving in 2005 to the HNK Hajduk Split academy.
After a season there, he wasn't given a professional contract and was released on a free transfer, only to be snapped up by NK Zagreb, led by Miroslav Blažević who saw in the young player a way to get back at Hajduk's chairman Branko Grgić – who shares his surname, and who had previously sacked Blažević, claiming that he was better than Luka Modrić.
[1] Grgić debuted against Hajduk, coming in the 19.8.2006 away fixture for Ivan Lajtman at the half-time of the 2–0 loss, managing a yellow card 10 minutes after.
[citation needed] He remained at the club until the beginning of 2010, when he moved to NK Međimurje, with whom he was relegated to the Druga HNL.
Recalled to Široki Brijeg, he spent the following autumn there, but achieved only two caps there before being sent back on loan to NK GOŠK Gabela, where he would go on to sign a professional contract in the summer of 2012.