Since the start of the coronavirus 2019 pandemic, people have faced many challenges, including in relation to sleep quality and psychological health. This study aims to analyze the association between sleep quality and psychological symptoms among university students in China, and to provide reference data to facilitate the development of interventions to improve the physical and mental health of university students. A stratified cluster sampling method was used to investigate the sleep quality and psychological symptoms of 6,363 university students in China. The Chi-square test was used to analyze differences in sleep quality among groups. Logistic regression analysis was used to analyze the association between sleep quality and psychological symptoms. The proportions of Chinese university students with good, medium, and poor sleep quality were 25.73, 10.99, and 63.28%, respectively. The overall rate of psychological symptoms was 16.5%. Logistic regression analysis showed that, in general, university students with poor sleep quality had a higher risk of psychological symptoms than those with good sleep quality (OR = 1.53, 95%CI: 1.28, 1.84, p < 0.01). Compared with university students with good sleep quality, those with poor sleep quality were more likely to experience emotional symptoms (OR = 1.62, 95%CI: 1.36, 1.94), behavioral symptoms (OR = 1.55, 95% CI: 1.3, 1.84), and difficulties with social adaptation (OR = 1.84, 95% CI: 1.51, 2.25) (all p < 0.01). There was an association between sleep quality and psychological symptoms among Chinese university students. University students with poor sleep quality have a higher risk of psychological symptoms. Measures should be taken to improve the sleep quality of university students and reduce the incidence of psychological symptoms. This study provides reference data for government and education departments that could inform public health policies.