In this paper, we proposed GaN trench Static Induction Transistor(SIT). Because The compound semiconductor had superior thermal characteristics, GaN and SiC power devices is next generation power semiconductor devices. We carried out modeling of GaN SIT with 2-D device and process simulator. As a result of modeling, we obtained 340 V breakdown voltage. The channel thickness was 3 urn and the channel doping concentration is $1e17;cm^{-3}$. And we carried out thermal characteristics, too.