Background: Although cross-sectional studies on the learning status of nursing undergraduates during the COVID-19 epidemic have surged, few studies have explored the normalization of COVID-19 on students’ learning burnout and mental health. The study was designed to investigate the learning burnout of nursing undergraduates in school under the normalization of the COVID-19 epidemic and explore the hypothesized mediation effect of academic self-efficacy in the relationship between anxiety, depression and learning burnout in Chinese nursing undergraduates. Methods: A cross-sectional study was conducted among nursing undergraduates in the school of nursing of a university in Jiangsu Province, China (n = 227). A general information questionnaire, College Students’ Learning Burnout Questionnaire, Generalized Anxiety Disorder Scale (GAD-7), and Patient Health Questionnaire depression scale (PHQ-9) were administered. Descriptive statistical analysis, Pearson correlation analysis, and multiple linear regression analysis were performed via SPSS 26.0. Process plug-in (Model 4) was used to test the mediating effect of academic self-efficacy (bootstrap 5000 iterations, α = 0.05). Results: Learning burnout (54.1 ± 0.656) was positively correlated with anxiety (4.6 ± 0.283) and depression (5.3 ± 0.366) (p < 0.01) and was negatively correlated with academic self-efficacy (74.41 ± 0.674) (p < 0.01). Academic self-efficacy plays a mediating role between anxiety and learning burnout (0.395/0.493, 80.12%) and a mediating role between depression and learning burnout (0.332/0.503, 66.00%). Conclusion: Academic self-efficacy has a significant predictive effect on learning burnout. Schools and teachers should strengthen the screening and counselling of students’ psychological problems, detect learning burnout caused by emotional problems in advance and improve students’ initiative and enthusiasm for learning.