The perturbation of atmosphere turbulence is a significant challenge in orbital angular momentum shift keying-based free space optical communication (OAM-SK-FSO). In this study, we propose an adaptive optical demodulation system based on deep learning techniques. A conditional convolutional GAN (ccGAN) network is applied to recover the distorted intensity pattern and assign it to its specified class. Compared to existing methods based on convolutional neural networks (CNNs), our network demonstrates powerful capability in recovering the distorted light beam, resulting in a higher recognition accuracy rate under the same conditions. The average recognition accuracy rates are 0.9928, 0.9795 and 0.9490 when the atmospheric refractive index structure constant $C_n^2$ is set at 3 × 10-13, 4.45 × 10-13, 6 × 10-13m-2/3, respectively. The ccGAN network provides a promising potential tool for free space optical communication.