Recent years have seen increased research interest in replacing the computationally intensive Magnetic resonance (MR) image reconstruction process with deep neural networks. We claim in this paper that the traditional image reconstruction methods and deep learning (DL) are mutually complementary and can be combined to achieve better image reconstruction quality. To test this hypothesis, a hybrid DL image reconstruction method was proposed by combining a state-of-the-art deep learning network, namely a generative adversarial network with cycle loss (CycleGAN), with a traditional data reconstruction algorithm: Projection Onto Convex Set (POCS). The output of the first iteration's training results of the CycleGAN was updated by POCS and used as the extra training data for the second training iteration of the CycleGAN. The method was validated using sub-sampled Magnetic resonance imaging data. Compared with other state-of-the-art, DL-based methods (e.g., U-Net, GAN, and RefineGAN) and a traditional method (compressed sensing), our method showed the best reconstruction results.