The asymptotic solutions of the paraxial equation for a combined electromagnetic concentric spherical system have been explored. Expressions of each kind of coefficients of two special solutions given by the asymptotic method for solving the paraxial equation have been deduced. By verifying the exact solution of two special solutions of the combined electromagnetic concentric spherical system, this paper proves that the approach based on asymptotic solutions given by Monastyrski ［Journal of Technical Physics, 1978, 48(6): 1117-1122］to solve the two special solutions of paraxial equation in electron optics is basically correct and feasible, and only a few aspects need to be improved.