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Despite that convolution neural networks (CNN) have recently demonstrated high-quality reconstruction for video super-resolution (VSR), efficiently training competitive VSR models remains a challenging problem. It usually takes an order of magnitude more time than training their counterpart image models, leading to long research cycles. Existing VSR methods typically train models with fixed spatial and temporal sizes from beginning to end. The fixed sizes are usually set to large values for good performance, resulting to slow training. However, is such a rigid training strategy necessary for VSR? In this work, we show that it is possible to gradually train video models from small to large spatial/temporal sizes, i.e., in an easy-to-hard manner. In particular, the whole training is divided into several stages and the earlier stage has smaller training spatial shape. Inside each stage, the temporal size also varies from short to long while the spatial size remains unchanged. Training is accelerated by such a multigrid training strategy, as most of computation is performed on smaller spatial and shorter temporal shapes. For further acceleration with GPU parallelization, we also investigate the large minibatch training without the loss in accuracy. Extensive experiments demonstrate that our method is capable of largely speeding up training (up to $6.2\times$ speedup in wall-clock training time) without performance drop for various VSR models. The code is available at https://github.com/TencentARC/Efficient-VSR-Training.