Irradiation uniformity of laser on target is very important for inertial confinement fusion (ICF). The theory of smoothing by spectral dispersion (SSD) in ICF is studied by translation theory of optic, and with whether using of SSD and different parameters of SSD, the variations of irradiation nonuniformity of the surface of target are numerically simulated combined with random phase plate (RPP). The results show that application of SSD can reduce the irradiation nonuniformity of the surface of target, the variations of irradiation nonuniformity with the time are oscillating at the beginning and drive to a constant in the end. When the number of color cycle is small, the broader of laser bandwidth and the better effect of SSD are obtained.