In order to study effect of atmospheric turbulence and avalanche photodiode (APD) noise when an APD receiving laser transmitted in turbulent atmosphere, both processes, i.e., laser propagation in turbulent atmosphere and laser detection by APD were analyzed. Then, combined with the detection principle of APD, the exponential Weibull-Gauss dual stochastic process model was established. The probability density of APD output current under different signal-to-noise ratios and atmospheric turbulence was measured. Different detection distances and receiving apertures were simulated. The results show that, when the received signal-to-noise ratio is 2, 5 and 10, the variances of light intensity distribution are 0.5354, 0.3565 and 0.2781, respectively and the offsets are 0.05, 0.0109 and 0.0029, respectively. When the structure constants of atmospheric refractive index are 2.5×10-15,3×10-14,4.9×10-14, the variances are 0.1198, 0.2781 and 0.4035, respectively and the offsets are 0.0002, 0.0029 and 0.0039, respectively. The dual stochastic process model can accurately describe the process for APD detecting laser transmitting in turbulent atmosphere. The change of detector aperture has little effect on the probability density of APD output current. With the increase of the received signal-to-noise ratio, detection distance and atmospheric refractive index structure constant, the average output current of APD is larger than that of signal current. And the degree of dispersion is aggravated. The establishment of this model has a certain reference value for the research of laser detection technology.