To acquire coefficients of Zernike polynomials is a discrete ill-posedness problem. Common methods, such as Least Squares Error method, Cram-Schmidt orthogonalization method and Householder transformation method, can not obtain a stable numerical solution. The instability of ill-posedness problem is analyzed and a Tikhonov regularization method is introduced to solve ill-posed problem. The L curve criterion is used to determine regularization parameter. Simulation result shows that Tikhonov regularization method is stable and effective for solving ill-posedness problem.