A numerical method for directly obtaining discrete relaxation modulus from static creep tests data is developed for linear viscoelastic asphalt mixtures. To overcome the ill-posedness of interconversion between creep compliance and relaxation modulus, Volterra integral equations of the second kind and L-curve based Tikhonov’s regularization method are used to construct the computational scheme of parameter estimation. A numerical case study is presented to demonstrate the efficiency of the regularization method, which takes into account different step lengths and noise levels. It indicates that the computed results are accurate and robust at different noise levels. Compared with other existing methods, the L-curve based Tikhonov’s regularization method provides the best parameter estimates in dealing with both the numerical case study and the experiment data. The method can be used to extract viscoelastic parameters of asphalt mixtures from creep tests effectively and robustly.