A compact two-dimensional(2-D) finite-difference frequency-domain method is used to analyze propagation characteristics of generalized ridge waveguides for the first time. Only four transverse field components are involved in the final resulting eigenvalue problem, so the required CPU time is reduced considerably as compared to the approaches by which six field components are comprised. Additionally, the feature of finding the phase constant for a given frequency is more pertinent in practical applications. To deal with the generalized ridge waveguides, we divide complex structure into several regular sub-regions, and apply the compact 2-D FDFD method respectively in every sub-region only by setting boundary conditions accordingly. Finally, the calculated numerical results in the current study show good agreement with the published ones in this field.