Abstract: In order to study the dynamic evolution and self-deflection of matching Gaussian beam in two-photon photorefractive media in external electric field, numerical simulation was used to obtain the dynamic evolution process and self-deflection graphics. The obtained results indicate that matching Gaussian beam can evolve into steady-state solitary wave for a given two-photon photorefractive crystal and the diffusion effect can cause self-deflection for the matching Gaussian beam. At first, the degree of self-deflection of matching Gaussian beam increases with the external electric field, however it decreases with the external electric field after a certain point. The relation between the degree of self-deflection of matching Gauss beam and the intensity of incident light is similar to external electric field.