This paper proposes and demonstrates an optical quantum random number generator based on distribution of single photon pulse amplitude of a photomultiplier tube.The ligh t emitted from ultraviolet LED is attenuated into discrete single photon sequence.After these photons are detecte d by the photomultiplier tube,the single-photon pulses with random distribution are output.Digital val ues of peaks of these single-photon pulses are used as the entropy sources of random number generation.In order to reduce the bias of the raw extracted random number,the SHA-256post processing method based on FPGA is proposed and implemented.When our designed quantum random number generator works at a counting rate of 500kc/s,7random bits can be extracted on average per detected photon,and a random number generation rate of 3.5Mbit/s is obtained.The random bit sequences are tested by random number test programs ENT and STS.The test res ults show that the generated random bit sequences fully meet the standards of true random numbers.