The dispersion relation of transverse magnetic（TM） wave and transverse electric（TE） wave for surface plasmon at a metal-Kerr nonlinear medium interface are analyzed based on the Maxwell equations and the boundary conditions. The dispersion relation of TM wave is complex, due to the nonlinearity, and it has a dielectric coefficient and intensity-dependent expression. However, the TE wave does not exist at this interface as in the linear case.