Deep learning-based methods have achieved promising results in single image super-resolution (SISR). However, the performance of existing deep SISR methods is very sensitive to image degradation. In addition, these methods are deterministic and do not introduce any uncertainty to the generated images, so we have no way of knowing the reliability of these generated images. To address these two challenging issues, we propose a model-agnostic approach for existing deep SISR networks to improve their robustness under various degradations. Our proposed method follows a probabilistic framework and applies Monte Carlo dropout to existing deep SISR methods. Instead of performing point estimation, the proposed method predicts the posterior distribution of super-resolved images. Based on this, we can determine the uncertainty of the generated images. Experiment results show that the proposed method can effectively improve the robustness of existing deep SISR methods, leading to state-of-the-art performance when applied to images having different degradations. The code is available at https://github.com/YangTracy/MCD-SR.