In this paper, we numerically study the propagation characteristics through spatial filter and free space of small-bandwidth pulsed beams with smoothing by spectral dispersion (SSD) in high power solid-state laser system. The numerical simulation with time-, space-and spectrum-resolution is achieved by using laser propagation and amplification software developed by Research Center of the Laser Fusion. The graphs of corresponding time-, space-and spectrum-distribution are presented, and the propagation characteristics between the SSD and non-SSD beam are compared. Besides, the effects of some SSD parameters on the diffraction propagation are further discussed. The results can help to choose the proper beam divergence of SSD which matches with the size of the spatial filter hole, to design the appropriate modulation frequency and the color circle number and so on. Moreover, it could guide the design of the light path, especially the design of free space propagation of small-diameter laser.