In this paper, we design and analyze a Ka-band microstrip line to rectangular waveguide transition using the expanding-cell FDTD method. The transition under investigation consists of a ridged waveguide, microstrip line, and $lambda$/4 Chebyshev impedance transformer. To improve the accuracyand efficiency, the expanding-cell FDTD method is applied to analyze the characteristics of a ridged waveguide impedance transformer. To verify the accuracy of the expanding-cell FDTD method, S parameters of the analyzed transition are compared with those of experimental data. The efficiency of the present approach is verified by comparing the computational time for expanding-cell and that for fine cell. The relation between the number of step and operation bandwidth is analyzed by comparing the characteristics of four and three step Chebyshev waveguide impedance transformer.