Laser-beam illumination uniformity is a key issue in inertial confinement fusion facilities. In order to fulfill the requirement of improving illumination uniformity, a radial smoothing (RS) scheme is proposed. For smoothing the focal-spot pattern on a short time scale compared with the hydrodynamic response time of the target, the optical Kerr effect with extremely response time is taken into consideration. The basic principle of RS based on optical Kerr effect is that by using the interaction between optical Kerr medium and periodic Gaussian pulses to modulate a periodic spherical phase, to modulate periodic sphericel phase added at the wavefront of laser transmission wave, change the focal-spot size of the laser beam in far field, and further induce the fast radial redistribution of the speckles inside the focal spot in far field, and further induce the fast radial redistribution of the speckles inside the focal spot in far field. This fast radial redistribution of the speckles smoothes the intensity modulation of the focal spot on the target and eventually achieves the beam smoothing in the radial direction. The application of RS in the beamline is detailed. The optical Kerr medium is inserted in the front-end of the bemline, before the laser beam is injected into the main amplifier. The periodic Gaussian pulse for pumping the optical Kerr medium is obtained by the pulse stacking system based on fibers. The pulse width of stacked Gaussian pulse and the time delay between Gaussian pulses are set to be on a picosecond time scale or subpicosecond time scale. The induced refractive index of the optical Kerr medium by the pump laser fits spherical distribution with periodic variation, and results in the radial distribution of the speckles in focal plane. By establishing the theoretical model of the radial beam smoothing scheme implemented with continuous phase plate (CPP), the focusing characteristics of laser beam with RS and CPP are discussed in detail. The influences of the selection of optical Kerr medium and the characteristics of the radial redistribution on the radial smoothing effect are simulated and analyzed. Results indicate that the RS based on optical Kerr effect could efficiently achieve the periodic radial redistribution of the speckles on focal plane, and therefore improves the illumination uniformity in the radial direction while eliminating the stripe pattern presented in far field by one-dimensional smoothing spectral dispersion (SSD). The smoothing performance of RS is different from that of the conventional SSD due to its radial smoothing direction. Moreover, the combined application of RS with continuous phase plate could achieve a better smoothing level with a shorter time. The utilization of radial smoothing scheme in high power laser system may significantly improve the laser-beam irradiation with little influence on the performance of the beamline.