Hospital organisations aim to restore patients’ health and improve their comfort. Furthermore, nurses are obligated to provide quality nursing care to patients. A hospital’s positive culture, interpersonal caring behaviour, and organisational health are important factors related to nursing quality. This study aimed to identify the factors that affected the quality of nursing care and verify the mediating effect of hospital organisational health on the relationship between positive nursing organisational culture, caring behaviour, and quality of nursing care. Data were collected from 190 clinical nurses who had worked for over 6 months in a tertiary hospital located in C city, South Korea. Descriptive statistics, independent t-test and one-way analysis of variance, Scheffe’s post-hoc test, Pearson’s correlation coefficient, hierarchical regression, and Baron and Kenny’s 3-stage procedures were calculated via SPSS version 25.0. Mediating effects were verified via bootstrapping. Hospital organisational health (β = 0.47, p < 0.001), ‘satisfied’ in departmental satisfaction (β = 0.26, p = 0.034), ‘surgical ward’ (β = 0.15, p = 0.017), ‘operating room/delivery room’ (β = 0.13, p = 0.023), ‘neonatal intensive care unit/nursery’ (β = 0.13, p = 0.039), and ‘outpatient department’ (β = 0.14, p = 0.018) in department of work were all factors that affected the quality of nursing care. Furthermore, these had significant effects, with an explanatory power of 57.2% (F = 10.70, p < 0.001). Hospital organisational health had a full mediating effect on the relationship between positive nursing organisational culture and quality of nursing care (B = 0.27, 95% BootCI = 0.18–0.37), as well as between caring behaviours among nurses and quality of nursing care (B = 0.21, 95% BootCI = 0.14–0.28). Practical measures to enhance nursing quality based on these findings should improve work and environmental conditions at the organisational level. In addition, measures to foster and manage a positive nursing organisational culture and promote various caring behaviour enhancement programs to improve hospital organisational health are recommended.