Constant bit rate (CBR) videos are widely used in streaming playback applications. However, the image quality of the CBR video is often unstable, especially for scenes with large motion. To this end, we design a new model to represent the distortion of High Efficiency Video Coding (HEVC) constant bit rate video, and propose a neural network for a constant bit rate video quality enhancement (CBREN). We propose a dual-domain restoration module (DRM) to jointly learn the prior knowledge in the pixel domain and the frequency domain. To address the degradation resulting from compression, we propose a twostep quantization degradation estimation strategy. The Inverse DCT (IDCT) Translation Unit (ITU) is used to constrain the quantization table of the constant bit rate video to a suitable range, and the Dynamic Alpha Unit (DAU) is used to finetune the quantization table according to the content of each frame. In order to effectively reduce the block distortion of different sizes produced in the compression process, we adopt a multi-scale network. Extensive experiments show that our approach can greatly enhance the quality of CBR compressed video. Moreover, our method can also be applied to constant quantization parameter (CQP) video enhancement tasks, and is certainly superior to existing methods.