Aiming at the problem that atmospheric laser communication is easily affected by atmospheric turbulence, which will lead to the degradation of communication quality, RNN and LSTM were established based on deep learning to predict refractive index structure constant, one of the most important parameters of atmospheric turbulence. Based on it, reference for the selection of atmospheric laser communication channels can be provided to avoid waste of channel resources. Three statistical values average absolute error, root mean square error and correlation coefficient were used to analyze the prediction results. The results showed that both RNN and LSTM can predict very well under medium and strong turbulence. The correlation coefficient between the predicted data and the original data were 67.37% and 96.17%.