In the scheme of radial smoothing based on the optical Kerr effect, pump laser pulse train uses optical Kerr effect of nonlinearity medium to add periodical spherical phase modulation, which makes the speckle inside the focal spot of the laser beam in far field sweep periodically at radial direction, and the uniformity of the focal spot in far field is improved. To analyze the influence of temporal characteristics change of the pump laser on beam smoothing effect, a theoretical model of the radial smoothing scheme has been established, and the time characteristic parameters of the pump laser has been analyzed and optimized. The results indicate that, for the given delay time between pump photon pulses, the sub-pulse with either too large or too small pulse width will reduce the irradiation uniformity of laser beam in far field. Meanwhile, with the increase of the pulse width of sub-pulse, the volatility of irradiation uniformity of laser beam in far field with integral time is trending toward stability relatively. Thus, the relatively large pulse width of the pump laser would be beneficial to obtain a more stable smoothing effect under the condition that the obvious beat wave effect should be avoided as far as possible. The time synchronous precision between the laser beam and the pump laser has a significant influence on the initial beam smoothing effect. For the pump laser of about one fifth period of the pulse train in advance, a better smoothing effect can be obtained in a relatively shorter integral time. In addition, for different temporal shapes of the pump laser, different smoothing effects can be achieved. When the temporal shape of the pump laser is triangular, the radial direction sweeping speed of the speckle inside the focal spot is relatively stable, and the radial smoothing effect and its stability can be improved effectively.