A theoretical model of numerical simulation of an adaptive optics (AO) system by modal wavefront reconstruction (i.e. by means of the Zernike polynomials expansion) is presented and the corresponding computer program is compiled. The AO computer program is combined with our simulation computational program of atmospheric propagation of laser beam to carry out a lot of simulation computations. It is found for the first time that there is an optimum term number of Zernike polynomials expansion. When the term number of Zernike polynomials expansion is higher than a certain value, results become worse very quickly. Zernike polynomials expansions of vertical arrangement and declined arrangement can give quite similar results. 15 terms of Zernike polynomials expansion which is thought usable in the wavefront reconstruction in literature, in fact can not give a correct result. The optimum term number gets lower as transverse wind speed is larger and the results of AO phase compensation by means of the model wavefront reconstruction with optmium term number are slightly better than those by means of the direct wavefront gradient control method.