This paper presents a numerical modeling of the temporal evolution of the refraction index induced by a nanosecond single laser pulse propagating in a biased photorefractive crystal. Assuming particular hypotheses typical for a short pulse illumination, a nonlinear time dependent partial differential equation, which describes the mechanisms of space–charge field build up and evolution, is derived from a mono-dimensional Kukhtarev band transport model. The numerical resolution of this space–charge equation is then coupled to the simulation of the propagation of a beam in a nonlinear medium using a beam propagation method. The results evidence the spatial self-focusing of a single nanosecond laser pulse. A description of the output beam profile evolution during the laser pulse is obtained and the role of different physical parameters such as the carriers mobility and the fluence on self-focusing is investigated. A successful comparison to previous experimental measurements is reported.