Objective. In the field of endoscopic imaging, Super-Resolution (SR) plays an important role in Manufactured Diagnosis, physicians and machine Automatic Diagnosis. Although many recent studies have been performed, by using deep convolutional neural networks on endoscopic SR, most of the methods have large parameters, which limits their practical application. In addition, almost all of these methods treat each channel equally based on the real-valued domain, without considering the difference among the different channels. Our objective is to design a SR model named Quaternion Attention Multi-scale Widening Network (QAMWN) for endoscopy images to address the above problem. Approach. QAMWN contains a stacked Quaternion Attention Multi-Scale Widening Block, that composed of Multi-scale Feature Widening Aggregation Module (MFWAM) and Quaternion Residual Channel Attention (QRCA). The MFWAM adopts multi-scale architecture with step-wise widening on feature channels for better feature extraction; and in QRCA, quaternion is introduced to construct Residual Channel Attention Mechanism, which obtains adaptively scales features by considering compact cross-channel interactions in the hyper-complex domain. Main results. To verify the efficacy of our method, it is performed on two public endoscopic datasets, CVC ClinicDB and Kvasir dataset. The experimental results show that our proposed method can achieve a better trade-off in model size and performance. More importantly, the proposed QAMWN outperforms previous state-of-the-art methods in both metrics and visualization. Significance. We propose a lightweight SR network for endoscopy and achieves better performance with fewer parameters, which helps in clinical diagnosis of endoscopy.