Retinal fundus images are widely used for the clinical screening and diagnosis of eye diseases. However, fundus images captured by operators with various levels of experience have a large variation in quality. Low-quality fundus images increase uncertainty in clinical observation and lead to the risk of misdiagnosis. However, due to the special optical beam of fundus imaging and structure of the retina, natural image enhancement methods cannot be utilized directly to address this. In this paper, we first analyze the ophthalmoscope imaging system and simulate a reliable degradation of major inferior-quality factors, including uneven illumination, image blurring, and artifacts. Then, based on the degradation model, a clinically oriented fundus enhancement network (cofe-Net) is proposed to suppress global degradation factors, while simultaneously preserving anatomical retinal structures and pathological characteristics for clinical observation and analysis. Experiments on both synthetic and real images demonstrate that our algorithm effectively corrects low-quality fundus images without losing retinal details. Moreover, we also show that the fundus correction method can benefit medical image analysis applications, e.g., retinal vessel segmentation and optic disc/cup detection.