A broadband reflection polarization converter in the terahertz frequency regime is proposed based on the L-shaped microstructured cell arrays. The characteristics of this polarization converter composed of L-shaped microstructured cell array, dielectric layer, and metal plates are numerically analyzed. The results demonstrate that the proposed polarization converter can not only convert a linearly polarized (LP) wave into a cross-polarized wave, but also convert LP waves into circularly polarized (CP) waves at two specific frequencies. In the frequency range of 0.64-1.19 THz, the polarization conversion ratio (PCR) is more than 80%, and the maximum PCR is more than 95%. In addition, the proposed converter can maintain a good polarization conversion performance under certain oblique incidence conditions.