We report the growth and characterization of group III-nitride semiconductor layers on graphene grown by chemical vapour deposition. GaN, AlGaN alloys, and InN layers are grown using an AlN nucleation and a buffer layer. We investigate the effect of varying growth temperature and V/III ratio and show that under optimized growth conditions preferentially semipolar $\mathrm{}\stackrel{}{\mathrm{}}\mathrm{}$ oriented nitride layers can be obtained. These layers, though polycrystalline, are highly oriented and show strong room temperature photoluminescence, thus showing graphene to be a novel substrate for the growth of III-nitride materials.