The deep learning-based decoder of polar codes is investigated over free space optical (FSO) turbulence channel for the first time. The feedforward neural networks (NN) are adopted to establish the decoder and some custom layers are designed to train the NN decoder over the turbulence channel. The tanh-based modified log-likelihood ratio (LLR) is proposed as the input of NN decoder, which has faster convergence and better bit error rate (BER) performance compared with the standard LLR input. The simulation results show that the BER performance of NN decoder with tanh-based modified LLR is close to the conventional successive cancellation list (SCL) decoder over the turbulence channel, which verifies that the NN decoder with tanh-based modified LLR can learn the encoding rule of polar codes and the characteristics of turbulence channel. Furthermore, the turbulence-stability is investigated and the trained NN decoder in a fixed turbulence condition also has stable performance in other turbulence conditions.