Video super-resolution aims at generating a high-resolution video from its low-resolution counterpart. With the rapid rise of deep learning, many recently proposed video super-resolution methods use convolutional neural networks in conjunction with explicit motion compensation to capitalize on statistical dependencies within and across low-resolution frames. Two common issues of such methods are noteworthy. Firstly, the quality of the final reconstructed HR video is often very sensitive to the accuracy of motion estimation. Secondly, the warp grid needed for motion compensation, which is specified by the two flow maps delineating pixel displacements in horizontal and vertical directions, tends to introduce additional errors and jeopardize the temporal consistency across video frames. To address these issues, we propose a novel dynamic local filter network to perform implicit motion estimation and compensation by employing, via locally connected layers, sample-specific and position-specific dynamic local filters that are tailored to the target pixels. We also propose a global refinement network based on ResBlock and autoencoder structures to exploit non-local correlations and enhance the spatial consistency of super-resolved frames. The experimental results demonstrate that the proposed method outperforms the state-of-the-art, and validate its strength in terms of local transformation handling, temporal consistency as well as edge sharpness.