Measurement-device-independent quantum key distribution(MDI-QKD) eliminates all loopholes on detection.Previous experiments of time-bin phase-encoding MDI-QKD allow a factor of 3/4 loss in the final key for the incapability of identifying two successive detection events by a single photon detector.Here we propose a new scheme to realize the time-bin phase-encoding MDI-QKD.The polarization states are used to generate the time bins and the phase-encoding states.The factor of loss in the final key is eliminated by using four single photon detectors at the measurement site.We show the feasibility of our scheme with a proof-of-principle experimental demonstration.The phase reference frame is rotated extremely slowly with only passive stabilization measures.The quantum bit error rate can reach 0.8% in the Z-basis and 26.2% in the X-basis. Measurement-device-independent quantum key distribution (MDI-QKD) eliminates all loopholes on detection. Previous experiments of time-bin phase-encoding MDI-QKD allow a factor of 3/4 loss in the final key for the incapability of identifying two successive detection events by a single photon detector. Here we propose a new scheme to realize the time-bin phase-encoding MDI-QKD. The polarization states are used to generate the time bins and the phase-encoding states. factor of loss in the final key is eliminated by using four single photon detectors at the measurement site. We show the feasibility of our scheme with a proof-of-principle experimental demonstration. The phase reference frame is rotated extremely slowly with only passive stabilization measures. The quantum bit error 0.8% in the Z-basis and 26.2% in the X-basis.