Magnetic Resonance Imaging (MRI) is a widely used medical diagnosis technique. However, the quality of MR image is affected by the noise which is caused by mechanical and environmental reasons during the MR image acquisition process. For decades, various kinds of methods including filtering approaches, transform domain approaches and statistical approaches have been applied to the MR image denoising problem, while there are also some drawbacks exiting in these methods such as arising undesirable change of texture and long computation time needed. In this paper, we proposed a novel MR image denoising method called DESN which is a neural network method and has a novel network architecture with well-designed loss function. In DESN, the convolutional neural networks itself is considered as a regularizer or image prior information for the inverse problems such as denoising. The network architecture of DESN is designed from the auto-encoder architecture, it has three main parts: encoder network for extracting low-resolution image features, decoder network for restoring high-resolution features and skip connections for transmitting abstract information from encoder network to decoder network. Besides, we also design a novel loss function which contains two main parts: data fidelity loss (), image quality penalty () and three loss terms: mean squared error term (), image structure similarity term (), image information entropy term (). We compare the performance of DESN with DIP and some state of the art denoising methods, and the performance of our network with different loss terms are also compared in three MR modalities. The comparative results show that DESN have the superior performance in generating high-quality MR image with enough edge and texture information.