Measurement-device-independent quantum key distribution (MDI-QKD) has received much attention, with the goal of overcoming all of the security loopholes caused by an imperfect detection system. We here propose a plug-and-play MDI-QKD (P&P MDI-QKD) scheme whereby an untrusted relay node, Charlie, owns a laser and sends photons to Alice and Bob. Alice (Bob) modulates the polarization of the incident photons and returns them to Charlie. Charlie uses a modified Bell state analyzer (BSA) to perform Bell state measurements (BSM). In comparison with the original version of MDI-QKD, our scheme exploits a single untrusted laser as the photon source. This makes the signal photons identical and enhances the Hong-Ou-Mandel effect. Second, because of the P&P structure, the setup can automatically eliminate the birefringence influence of the fibers, which makes the setup highly stable. Finally, our modified BSA can identify vertical bar phi >+ and vertical bar phi >- of four Bell states with polarization encoding but not vertical bar psi >+ and vertical bar psi >-. Based on practical experimental parameters, a simulation showed that the maximum theoretical secure transmission distance could reach more 280 km.