Abstract:The phase modulate free measurement device independent quantum key distribution is proposed in this paper.When the phase drifts slowly and time-varying,this pr otocol does not need the assistant alignment subsystem to share the same referen ce frame,which reduce the system complexity to some extent.The secure key rate a nd maximal transmission distance of the phase modulate free measurement device i ndependent quantum key distribution are analyzed,with weak coherent source and p arametric down conversion source,respectively,Meanwhile,the statistical fluctuat ion caused by finite-size key is taken into account,which has impact on the sec ure key generation rate.Numerical simulations show that the maximal transmission distance of phase modulate free measurement device independent quantum key dist ribution is close to that of original measurement device independent quamtum key distribution.Furthermore,when get the nearly maximal transmission distance,the length of pulse needed by phase modulate free indepenent measurement device inde pendent quamtum key distribution is five orders of magnitude shorter than that o f original measurement device independent quamtum key distribution protocol,whic h improve the system efficiency.