The possibilities of numerical method for solving of wave equation of gradient planar waveguide in a frequency domain are investigated. The method is based on the Fourier transform of wave equation and on a solution of transformed equation by numerical method. Finally, a task of finding of propagation constants and Fourier transforms of fields in a discrete form is reduced to the eigenvalue/eigenvector problem. Comparison of searching results of propagation constants obtained by the proposed method, approximate Wentzel–Kramers–Brillouin method and accurate analytical methods for some waveguides is carried out. The new method provides a high accuracy when the Nyquist–Shannon sampling theorem is done, and it is characterized by a high numerical stability.