Abstract The past few years have witnessed great success in applying deep learning to enhance the quality of compressed image/video. The existing approaches mainly focus on enhancing the quality of a single frame, ignoring the similarity between consecutive frames. In this paper, we investigate that heavy quality flfluctuation exists across compressed video frames, and thus low quality frames can be enhanced using the neighboring high quality frames, seen as Multi-Frame Quality Enhancement (MFQE). Accordingly, this paper proposes an MFQE approach for compressed video, as a fifirst attempt in this direction. In our approach, we fifirstly develop a Support Vector Machine (SVM) based detector to locate Peak Quality Frames (PQFs) in compressed video. Then, a novel Multi-Frame Convolutional Neural Network (MF-CNN) is designed to enhance the quality of compressed video, in which the non-PQF and its nearest two PQFs are as the input. The MF-CNN compensates motion between the non-PQF and PQFs through the Motion Compensation subnet (MC-subnet). Subsequently, the Quality Enhancement subnet (QE-subnet) reduces compression artifacts of the non-PQF with the help of its nearest PQFs. Finally, the experiments validate the effectiveness and generality of our MFQE approach in advancing the state-of-the-art quality enhancement of compressed video. The code of our MFQE approach is available at https://github.com/ryangBUAA/MFQE.git