Using the full-potential linearized augmented plane wave method within the generalized gradient approximation, we investigatete the electronic structures, magnetisms and half-metallicities of the full-Heusler X2YGa (X=Co, Fe, Ni; Y=V, Cr, Mn) alloys. It is found that the spin-orbit coupling has little effect on the electronic structures, magnetisms and half-metallicities of the full-Heusler X2YGa (X=Co, Fe, Ni; Y=V, Cr, Mn) alloys. Without spin-orbit coupling the Co2VGa,Co2CrGa,and Fe2CrGa alloys are half-metallic or nearly half-metallic ferromagnets. With including the spin-orbit coupling, the spin-polarizations are lowered by about 1%, thus they still remain high spin-polarizations. The Fe2MnGa, Co2MnGa, Ni2CrGa, and Ni2MnGa alloys are conventional ferromagnets, whereas the Fe2VGa and Ni2VGa alloys are paramagnets.