Graphene-on-silicon field-effect transistors (GOSFETs) are studied as a candidate of next generation transistors. Graphene is formed on SiC layers grown on Si substrates. As well as the channel material, the gate stack is also a key component of FETs. In this study, SiCN deposited by plasma-enhanced chemical vapor deposition (PECVD) using hexamethyldisilazane (HMDS) vapor is studied. During PECVD, hydrogen is used as a carrier gas in addition to HMDS vapor. This becomes an advantage in the graphene process because hydrogen has cleaning effect on graphene surface. To verify this effect, SiCN gate stack is applied to the graphene on SiC substrates. FETs with SiCN gate stack exhibit clearer ambipolar characteristics and larger drain current density than FETs with conventional SiN gate stack. The SiCN gate stack is also applied to GOSFETs. Resulting devices also exhibit ambipolar characteristics and larger current density than previously reported GOSFETs with SiN gate stack.