In this paper, we present an analysis of microstrip line with a trapezoidal dielectric ridge in multilayered media. The method employed in this characterization is called partial-boundary element method (p-BEM) which provides an efficient technique to the analysis of the structures with multilayered media. To improve the convergence of the Green's function used in the analysis with the P-BEM, we employ a technique based on a combination of the Fourier series expansion and the method of images. Treatment on convergence for the boundary integrals is also described. After this treatment, it requires typically one tenth or one hundredth of Fourier terms to obtain the same accuracy compared with the original Green's function. Numerical results are presented for two microstrip lines that have a trapezoidal dielectric ridge placed on a one-layered substrate and a two-layered substrate. These numerical results demonstrate the effects on the characteristics of the microstrip line due to the existence of the dielectric ridge as well as the second layer between the ridge and the fundamental substrate.