Atmospheric transmission distortion is one of the main challenges hampering the practical application of a vortex beam (VB) which carries orbital angular momentum (OAM). In this work, we propose and investigate a deep learning based atmospheric turbulence compensation method for correcting the distorted VB and improving the performance of OAM multiplexing communication. A deep convolutional neural network (CNN) model, which can automatically learn the mapping relationship of the intensity distributions of input and the turbulent phase, is well designed. After trained with loads of studying samples, the CNN model possesses a good generalization ability in quickly and accurately predicting equivalent turbulent phase screen, including the untrained turbulent phase screens. The results show that through correction, the mode purity of the distorted VB improves from 39.52% to 98.34% under the turbulence intensity of Cn2 = 1 × 10-13. Constructing an OAM multiplexing communication link, the bit-error-rate (BER) of the transmitted signals in each OAM channel is reduced by almost two orders of magnitude under moderate-strong turbulence, and the demodulated constellation diagram also converges well after compensated by the CNN model.