Abstract: We study numerical method for relativistic Vlasov equation and present a scheme for computing Vlasov equation based on Cartesian-spherical coordinate system, which can be used to reduce number of numerical grid for momentum space. Furthermore, a 4th order non-splitting finite volume scheme is proposed in order to solve momentum parts of relativistic Vlasov equation. In test problems, especially relativistic Landau problem, laser-plasma interaction are solved by using the scheme. We confirm the scheme with theoretically analysis as well as numerical comparison with results of PIC method.