In its practical applications, quantum key distribution is affected by the finite detector dead time. When the signal pulse transmission rate is too large, the probability of detector's measurement failure increases and the security key generation rate decreases. In this paper, the finite detector dead time problem is analyzed for measurement-device-independent quantum key distribution under the heralded pair coherent state photon source. The relationship between the security key generation rate and the signal transmission rate is studied and simulated. Considering the detector's dead time, the secure key generation rate of the measurement-device-independent quantum key distribution protocol based on the heralded pair coherent state photon source is higher than that of the measurement-device-independent quantum key distribution protocol based on the weak coherent state photon source. In addition, the security key generation rates are analyzed with the respective finite detector's dead time τ of 50, 100, and 150 ns. The results show that the higher the detector's dead time is, the lower the limit value of the security key generation rate is. The relation between the limit value of the security key generation rate and the finite detector's dead time is 8.1×10 ³/τ.