The atmospheric turbulence phase screen generated using the conventional power-spectrum-inversion method shows insufficient low-frequency sampling. Whereas the phase screen can be generated using the direct-summation method, the simulation speed is low owing to the significant amount of computations involved. Herein, a deep-learning technique is introduced to efficiently simulate an atmospheric turbulence phase screen by training a deep convolutional generative-adversarial network (DCGAN) model. The generator and discriminator loss functions converge to 0.07 and 0.98, respectively, and the trained model can be used to directly generate turbulent phase screens. Two methods for generating the atmospheric turbulence phase screen, i.e., the conventional numerical simulation and a simulation based on the DCGAN model, were used. A comparison between the two reveals that the DCGAN model can alleviate the shortcomings of the conventional simulation method at low frequencies and overcome the periodicity limitation. This method is applicable to the rapid generation of atmospheric turbulence phase screens as well as to image simulation and emulation.