Due to the growth of research on sleep, mental health, and learning burnout on healthy growth and its related public health significance of adolescents, this study aimed to provide a deeper understanding of the effect of mental health and learning burnout on sleep among primary school students. The sleep quality (subjective sleep quality, sleep time, sleep latency, sleep duration, sleep efficiency, sleep disturbance, and daytime dysfunction), mental health, and learning burnout (exhaustion, learning cynicism, and reduced efficacy) of 900 students of grades 3–6 in primary schools were assessed in 2020. The PSQI scores of participants were 4.19 ± 2.545, of which a number of 322 (39.03%) students had sleep disturbance (PSQI scores ≧ 5). Binary logistic regression analysis showed that screen time (OR = 1.518, 95% CI: 1.164–1.980), ranking status (OR = 0.659, 95% CI: 0.480–0.907), learning burnout (OR = 1.088, 95% CI: 1.067–1.108), and mental health (OR = 4.672, 95% CI: 1.954–11.173) were the influencing factors for sleep quality of grade 3–6 students. According to the mediation effect analyses, mental health played a mediating effect (58.73% of the total effect) on the relationship between learning burnout and sleep quality. In conclusion, primary school students in Hunan of China have prominent sleep problems, and the daytime dysfunction caused by sleep problems is the most serious. Learning burnout positively predicted poorer sleep quality, and mental health played a mediating effect on the relationship between learning burnout and sleep quality.