Estimation of random errors, which are due to shot noise of photomultiplier tube(PMT) or avalanche photodiode(APD) detectors, is very necessary in lidar observation. Due to the Poisson distribution of incident electrons, there still exists a proportional relationship between standard deviation and square root of its mean value. Based on this relationship,noise scale factor(NSF) is introduced into the estimation, which only needs a single data sample. This method overcomes the distractions of atmospheric fluctuations during calculation of random errors. The results show that this method is feasible and reliable. Estimation of random errors, which are due to shot noise of photomultiplier tubes (PMT) or avalanche photodiode (APD) detectors, is very necessary in lidar observation. Due to the Poisson distribution of incident electrons, there still exists a proportional relationship between standard deviation and square root of its mean value. Based on this relationship, the noise scale factor (NSF) is introduced into the estimation, which only needs a single data sample. which results overcomes the distractions of that this method is feasible and reliable.