Downscaling is a critical step to bridge the gap between large‐scale climate information and local‐scale impact assessment. This study presents a novel deep learning approach: Super Resolution Deep Residual Network (SRDRN) for downscaling daily precipitation and temperature. This approach was constructed based on an advanced deep convolutional neural network with residual blocks and batch normalizations. The data augmentation technique was utilized to address overfitting that is due to highly imbalanced precipitation and nonprecipitation days and sparse precipitation extremes. Synthetic experiments were designed to downscale daily maximum/minimum temperature and precipitation data from coarse resolutions (25, 50, and 100 km) to a high resolution (4 km). The results showed that, during the validation period, the SRDRN approach not only captured the spatial and temporal patterns remarkably well, but also reproduced both precipitation and temperature extremes in different locations and time at the local scale. Through transfer learning, the trained SRDRN model in one region was directly applied to downscale precipitation in another region with a different environment, and the results showed notable improvement compared to classic statistical downscaling methods. The outstanding performance of the SRDRN approach stemmed from its ability to fully extract spatial features without suffering from degradation and overfitting issues due to the incorporations of residual blocks, batch normalizations, and data augmentations. The SRDRN approach is thus a powerful tool for downscaling daily precipitation and temperature and can potentially be leveraged to downscale any hydrologic, climate, and earth system data.