Retinal image quality assessment (RIQA) is essential for retinal examinations, as it impacts the certainty of both manual and intelligent diagnosis. Unfortunately, domain shifts, such as the variance of colors and illumination, are prone to confuse RIQA. Though efficient domain adaptation solutions have been proposed, properly transferring RIQA models to new domains remains a troublesome task. This paper presents a domain adaptative RIQA algorithm with knowledge distillation using a competitive teacher-student network (CTSN) to address the above issue. The main structure consists of a teacher network, a student network, and a competition module. The teacher network provides pseudo-labels by adapting source and target domain features, and the student network learns features from target-specific pseudo-labels. The competition module boosts the fine-grained adaptation of RIQA. Comparison experiments and ablation studies demonstrate that our method performs outstandingly in RIQA with domain shifts.