Basis dependence and statistical fluctuation of light sources are problems for the measurement-device-independent quantum key distribution protocol based on heralded single-photon source (HSPS). To solve these problems, in this work, the quantum key distribution protocol based on HSPS in Poisson distribution and orbital angular momentum (OAM) was studied. Moreover, its statistical fluctuation was analyzed. The relationship among the transmission efficiency, key generation rate, and safe transmission distance of the protocol under symmetric and asymmetric channels was examined. Furthermore, the effect of statistical fluctuation on the key generation rate and transmission distance was simulated. Simulation results show that the problem of basis dependence is solved by OAM coding, and the key generation rate and transmission distance of the protocol are improved. The effect of statistical fluctuation on the key generation rate of the protocol increases with the transmission distance. For the same number of pulses, the key generation rate and safe transmission distance under the asymmetric channel are greater than those under the symmetric channel.