Low-light videos are usually accompanied with acquisition noise, motion blur and some other specific distortions, which makes it hard to compress by the video coding technologies and generates less satisfying compressed videos. In order to enhance both the subjective and objective quality of compressed dark videos, we propose a novel learning based post-processing scheme for the most recent VVC. Specifically, we adopt a multi-scale residue learning structure, named Dark Video Restoration Convolutional Neural Network (DVRCNN), as an additional out-loop post-processing method. To avoid the over-smooth effect by MSE metric, SSIM and texture loss are also added to the final loss function. Luma and chroma components are decomposed then fed to two corresponding models separately. Compared with VVC baseline on the six sequences given in ICME 2020 Grand Challenge, our approach significantly reduces the BD-rate by 36.08% and achieves a fair promotion on both objective and subjective quality, especially for the low bit-rate compressed sequence with severe distortion. Validation results show that the proposed model generates well to continuous scenes and variable bitrates.