In the adaptive optical system, the gradient measuring error of Hartmann-Shack wave-front sensor is one of the main error sources affecting wave-front reconstruction precision. In this paper, the universality error transfer coefficient expression of modal wave-front reconstruction has been derived. Make use of the gradient data measured with Hartmann-Shack wave-front sensor in 61-element adaptive optical system, the correctness of the error transfer coefficient express of modal wave-front reconstruction has been proved.