It is simulated numerically the transmission of beams phase modulated and spectrally dispersed by the unit for smoothing by spectral dispersion put in the laser driver for inertial confinement fusion. The results show that the diffraction spot of a spectrally dispersed beam becomes larger and its near-field uniformity is improved, while there exists area where the intensity is nearly even within the far-field spot. The effects of the main parameters of the electro-optic phase modulator and the grating in the unit on the diffraction characteristics of the beams are further discussed, and it is found that intensity modulation emerges in the far-field spot under some conditions.