An extensive study on the in-loop filter has been proposed for a high efficiency video coding (HEVC) standard to reduce compression artifacts, thus improving coding efficiency. However, in the existing approaches, the in-loop filter is always applied to each single frame, without exploiting the content correlation among multiple frames. In this paper, we propose a multi-frame in-loop filter (MIF) for HEVC, which enhances the visual quality of each encoded frame by leveraging its adjacent frames. Specifically, we first construct a large-scale database containing encoded frames and their corresponding raw frames of a variety of content, which can be used to learn the in-loop filter in HEVC. Furthermore, we find that there usually exist a number of reference frames of higher quality and of similar content for an encoded frame. Accordingly, a reference frame selector (RFS) is designed to identify these frames. Then, a deep neural network for MIF (known as MIF-Net) is developed to enhance the quality of each encoded frame by utilizing the spatial information of this frame and the temporal information of its neighboring higher-quality frames. The MIF-Net is built on the recently developed DenseNet, benefiting from its improved generalization capacity and computational efficiency. In addition, a novel block-adaptive convolutional layer is designed and applied in the MIF-Net, for handling the artifacts influenced by coding tree unit (CTU) structure in HEVC. Extensive experiments show that our MIF approach achieves on average 11.621% saving of the Bjøntegaard delta bit-rate (BD-BR) on the standard test set, significantly outperforming the standard in-loop filter in HEVC and other state-of-the-art approaches.