The mental health of high-level athletes is a growing concern, especially in the context of the COVID-19 pandemic. Sleep is also an explicit health index closely related to mental health. This study aims to investigate the relationship between sleep, anxiety, depression, and perceived psychological stress among athletes, with a focus on sleep as a potential mediator in these mental health conditions. A comprehensive questionnaire included the Generalized Anxiety Disorder Scale-7 (GAD-7), Patient Health Questionnaire-9 (PHQ-9), Athlete Psychological Stress Questionnaire (APSQ), and Athlete Sleep Screening Questionnaire (ASSQ), and was administered to a sample of 501 elite Chinese athletes. Statistical analysis software and structural equation modeling were used to examine the characteristics, correlations, and influence pathways of the four indicators. The findings indicated that, compared to previous studies, the prevalence of perceived psychological stress (78.6%) and sleep disorders (24.8%) in the athlete sample were higher. All three mental health indicators were significantly positively correlated with sleep disorders. In terms of influence pathways, there was a direct path from APSQ to PHQ-9, with the direct effect of perceived stress on depression accounting for 32.5%. The indirect paths from APSQ to GAD-7 to PHQ-9 and from APSQ to GAD-7 to ASSQ to PHQ-9 accounted for 67.5%. Sleep disorders in competitive athletes are closely related to mental health, potentially serving as an important observable health behavior indicator and mediating factor in the transition from anxiety to depression. There is a need to strengthen comprehensive intervention measures that combine mental health and sleep health behaviors for athletes.