We have implemented a practical plug-and-play measurement-device-independent quantum key distribution (MDI QKD) system with polarization division multiplexing (PDM). MDI QKD is known as a secure protocol that can inherently prevent detection loopholes. Significant efforts have been made toward implementing MDI QKD systems. Recently, a plug-and-play architecture has been proposed for implementing the MDI QKD system, and its feasibility has been experimentally verified in both free space and fiber channel. However, in order to apply it to the real world, it is necessary to develop a more practical architecture including multiplexing methods and self-compensation techniques. In this paper, we have proposed and implemented a practical plug-and-play MDI QKD architecture that can be implemented regardless of whether the quantum channel lengths of Alice and Bob are symmetric or asymmetric using PDM and can be operated even under ambient-temperature-changing environments through an optical path-length self-compensation technique. Experimentally, we have achieved $6.25\times 10^{-6}$ bits per pulse as the key rate and the quantum bit error rates under 3% on 25-km quantum channels.