An efficient numerical method is proposed and implemented for the analysis of propagation characteristics of single-mode optical fibers with arbitrary refractive index profile. The method follows the concept of the so-called model-based parameter estimation, and the Pade algorithm is used to construct a low-order rational approximant of the spectral domain Green’s function, obtained by solving a hierarchy of static problems. The sought eigenfrequency and field distribution are then estimated by computing, respectively, the dominant pole and the related residual of the rational approximant. A number of profiles are analyzed and experiments show that very accurate results can be cheaply obtained through this technique.