The introduction of convolutional neural networks (CNNs) into single-image super-resolution (SISR) has resulted in remarkable performance in the last decade. There is a contradiction in SISR between indiscriminate processing and the different processing difficulties in different regions, leading to the need for locally differentiated processing of SR networks. In this paper, we propose an epistemic-uncertainty-based divide-and-conquer network (EU-DC) in order to address this problem. Firstly, we build an image-gradient-based divide-and-conquer network (IG-DC) that utilizes gradient-based division to separate degraded images into easy and hard processing regions. Secondly, we model the IG-DC’s epistemic uncertainty map (EUM) by using Monte Carlo dropout and, thus, measure the output confidence of the IG-DC. The lower the output confidence is, the more difficult the IG-DC is to process. The EUM-based division is generated by quantizing the EUM into two levels. Finally, the IG-DC is transformed into an EU-DC by substituting the gradient-based division with EUM-based division. Our extensive experiments demonstrate that the proposed EU-DC achieves better reconstruction performance than that of multiple state-of-the-art SISR methods in terms of both quantitative and visual quality.