The performance of any water projects depends on forecasting hydrological events in the future. In hydrology using physical models is not feasible to predict future events and often used from abstract model that describes the system based on mathematical concepts. The use of statistical distributions to estimate annual average discharge in different return periods  to design the hydraulic structures is one of the most common methods. In this research in order to obtain the best statistical distributions and estimate annual average discharge in different return periods, annual average discharge data from 6 hydrometric stations Gilan province named Punel, Rudbarsera, Toollat, Shalman, Mashinkhaneh and Haratbar were collected during the 50-year statistical periods (1965 to 2016). The randomness of the data was tested with Run Test method and then fitted with a variety of relevant statistical distributions using SMADA software based on the Method of Moments. Finally, the best distribution was determined using statistical indicators root mean square error (RMSE) and mean absolute error percentage (MAPE) for all hydrometric stations. The results showed that the mean annual discharge statistics of Punel, Shalman, Toollat, Mashinkhaneh and Haratbar stations with Log Pearson type III distribution and Rudbarsera station with 3Parameter Log Normal distribution Show the most fit and compliance. Therefore, using the best distributions mentioned above, return periods of 2, 3, 5, 10, 25, 50, 100 and 200 years were estimated.