Scintillation caused by atmospheric turbulence impairs the performance of the atmospheric optical communication system. Bit error rate(BER) of an atmospheric optical communication system can be improved by using an adaptive detection threshold, which is difficult to implement in real time. As a sub-optimum method, optimizing the threshold to a constant value according to statistics of parameters was proposed. Assuming multiplicative Gaussian noise and lognormal scintillation, the optimum constant threshold of an atmospheric optical communication in turbulence channel was analyzed. The result of numerical analysis was compared with experimental data obtained in weak turbulence. Results of experiment and numerical analysis show that optimizing constant threshold is necessary and the performance degradation compared to adaptive thresholding is acceptable. Neglecting aperture-averaging effects, the dependence of the optimum constant threshold on log amplitude variance and average received signal power was analyzed and the influence of other parameters was proved to be negligible. Based on previous analysis, a non-linear model was proposed to estimate the optimum constant threshold in practice.