To facilitate the transformation from conventional power systems towards smart grids, the concept of microgrids has been widely applied in practice, serving as the medium to accommodate renewable generators. One crucial problem is the stability associated with microgrids. This paper proposes a converter-based power system stabilizer (CBPSS), acting as a supplementary control loop, to enhance the stability of the islanded microgrids. The goal of the proposed CBPSS is to stabilize the critical microgrid mode with the generation of a damping torque, and it is achieved with the identification of the forward loop from the CBPSS to the microgrid. Then, the parameters of the proposed CBPSS can be designed accordingly to compensate the phase lag of the identified forward loop. Besides, an eigenvalue-mobility-based method is presented to identify the optimal installation location of the CBPSS in microgrids. As a consequence, the maximum stabilizing effect can be realized with the least control effort. Finally, modal analysis and time-domain simulations as well as hardware experimental results confirm the effectiveness of the proposed method.