A simple polarization converter using an L-figured waveguide is analyzed by the imaginary-distance beam-propagation method based on Yee's mesh and the finite-difference time-domain method. It is revealed at a wavelength of 1.55 m that the polarization conversion length is 3.24 m with an insertion loss of 0.46 dB. To achieve a wideband operation, we determine a device length by the effective index difference between the two eigenmodes generated in the L-figured waveguide. As a result, an extinction ratio of more than 20 dB is obtained over a wide wavelength range of 1.3 to 1.6 m. Finally, to reduce the insertion loss, we propose a modified structure, in which two corners in a diagonal position are cut with an angle of 90.