Compressed sensing magnetic resonance imaging (CS-MRI) has provided theoretical foundations upon which the time-consuming MRI acquisition process can be accelerated. However, it primarily relies on iterative numerical solvers, which still hinders their adaptation in time-critical applications. In addition, recent advances in deep neural networks have shown their potential in computer vision and image processing, but their adaptation to MRI reconstruction is still in an early stage. In this paper, we propose a novel deep learning-based generative adversarial model, RefineGAN, for fast and accurate CS-MRI reconstruction. The proposed model is a variant of fully-residual convolutional autoencoder and generative adversarial networks (GANs), specifically designed for CS-MRI formulation; it employs deeper generator and discriminator networks with cyclic data consistency loss for faithful interpolation in the given under-sampled -space data. In addition, our solution leverages a chained network to further enhance the reconstruction quality. RefineGAN is fast and accurate-the reconstruction process is extremely rapid, as low as tens of milliseconds for reconstruction of a image, because it is one-way deployment on a feed-forward network, and the image quality is superior even for extremely low sampling rate (as low as 10%) due to the data-driven nature of the method. We demonstrate that RefineGAN outperforms the state-of-the-art CS-MRI methods by a large margin in terms of both running time and image quality via evaluation using several open-source MRI databases.