A model of optical Kerr effect time gate is built. The CS2 Kerr signal curve obtained through the pump-probe experiment is acted as optical gate response function. The beam propagation is divided through time slicing and space distribution, and the temporal and spatial variation of the optical gate is given through the simulation. The width of the time gate and the spatial distribution of the beam are studied under different angles between the pump beam and the probe beam and different spatial distributions of the pulses. The results indicate that, for the pump beam and probe beam with Gaussian distribution, the time gate width becomes narrow with the intersection angle increasing between the pump beam and the probe beam, and the spatial distribution changes from roundness to ellipse. The bigger the intersection angle is, the bigger the ellipse degree is. If the spatial distributions of input pump beam and probe beam are super-Gaussian distribution, the rise edge of the temporal distribution becomes slow with increasing intersection angle between the pump beam and the probe beam, while the spatial distribution is unchanged, and the ellipse degree is about 1/3. The results provide reference for parameter design of experiments such as pump probe and time gated ballistic imaging.