An algorithm based on singular value decomposition (SVD) is presented to fit the wavefront with Zernike polynomials. In the current algorithm, SVD is applied to decompose the matrix of the linear equations directly. In the process of computing the inverse matrix, a threshold value is employed to modify the reciprocals of singular values which are zero or too small. Then the Zernike coefficients can be worked out immediately. Compared with the typical Gram-Schmidt orthogonalization, SVD has good stabilization when solving the least square problem of the ill-conditioned equations or singular matrix. And also because of avoiding construction of normal equation group, the computational error is eliminated. Moreover, it is quite easy to be programmed.