Abstract: The detector cannot detect photon successfully when the signal transmission rate exceeds the maximum detector count rate in high speed quantum key distribution scheme. This leads to correlations in the sifted bit string, and the security is compromised. In this paper, the high speed measurement device independent quantum key distribution based on BB84 protocol with finite detector dead time was analyed and the optimal transmission speed was simulated. Simulation result shows that the sifted key rate raised linearly with the increase of photon transmission rate without consideration of the influence of detector's dead time; with consideration of the influence of detector's dead time, the sifted key rate is no longer raising with the photon transmission rate infinitely and the curve of sifted key rate is distorted. When the transmission distance is 100 km, the correlation between the sifted key rate and detector dead time is approximate to 2.1/10, and the correlation between optimal transmission rate and detector dead time is approximate to 3.3105/.