Because of low frequency distorted wave front impacting on beam quality in ICF system, a thin mirror with diameter 300mm is optimized in order to compensate the distorted wave front. Meanwhile, the influences of low frequency distorted wave front made to laser beam quality are discussed in detail. Far field beam quality before and after compensating distorted wave front is discussed in detail, too. The analysis results show whether the space scale parameter of the low frequency wave front is altered or the amplitude of the wave front is changed, the amplitude of the wave front decrease obviously, phase gradient reduce during the whole spatial period, the peak of far field intensity increase, power focusability of focal spot is improved obviously.