Magnetic resonance imaging (MRI) as a critical clinical tool in medical imaging, requires a long scan time for producing high-quality MRI images. To accelerate the speed of MRI while reconstructing high-quality images with sharper edges and fewer aliases, a novel dual-domain generator and edge-enhancement dual discriminator generative adversarial network structure named DGEDDGAN for MRI reconstruction is proposed, in which one discriminator is responsible for holistic image reconstruction, whereas the other is adopted to enhance the edge preservation. A dual-domain U-Net structure that cascades the frequency domain and image domain is designed for the generator. The densely connected residual block is used to replace the traditional U-Net convolution block to improve the feature reuse capability while overcoming the gradient vanishing problem. The coordinate attention mechanism in each skip connection is employed to effectively reduce the loss of spatial information and enforce the feature selection capability. Extensive experiments on two publicly available datasets i.e., IXI dataset and CC-359, demonstrate that the proposed method can reconstruct the high-quality MRI images with more edge details and fewer artifacts, outperforming several state-of-the-art methods under various sampling rates and masks. The time of single-image reconstruction is below 13 ms, which meets the demand of faster processing.