Gaj-Grzmięca (Polish pronunciation: [ɡaj ˈɡʐmjɛntsa]) is a village in the administrative district of Gmina Zbiczno, within Brodnica County, Kuyavian-Pomeranian Voivodeship, in north-central Poland. It lies 5 kilometres (3 mi) east of Zbiczno, 11 km (7 mi) north of Brodnica, and 66 km (41 mi) north-east of Toruń.