In the inertial confinement fusion (ICF) system, continuous phase plate (CPP) designed by improved G-S algorithm can be used to improve the far-field distribution of distorted wave-front. Since the smoothing results of CPP for different distorted wave-fronts are different, the smoothing tolerance ability of CPP is analyzed systematically. According to the transmission characteristics of the distorted laser beams, root mean square (RMS) gradient of wave-front is used to quantify the wave-front distortion. And the far-field intensity distributions of different distorted beams which have translated through CPP are calculated by the numerical method. By comparing the uniformity of far-field focal spot after smoothing by CPP, a conclusion can be gotten that when the RMS gradient is under 0.32 wave/mm, CPP has good beam smoothing ability.