Most conventional supervised super-resolution (SR) algorithms assume that low-resolution (LR) data is obtained by downscaling high-resolution (HR) data with a fixed known kernel, but such an assumption often does not hold in real scenarios. Some recent blind SR algorithms have been proposed to estimate different downscaling kernels for each input LR image. However, they suffer from heavy computational overhead, making them infeasible for direct application to videos. In this work, we present DynaVSR, a novel meta-learning-based framework for real-world video SR that enables efficient downscaling model estimation and adaptation to the current input. Specifically, we train a multi-frame downscaling module with various types of synthetic blur kernels, which is seamlessly combined with a video SR network for input-aware adaptation. Experimental results show that DynaVSR consistently improves the performance of the state-of-the-art video SR models by a large margin, with an order of magnitude faster inference time compared to the existing blind SR approaches.