Applying the organisational climate of corporate social responsibility (CSR) and human resource management (HRM) behavioural theories, this paper examines the associations among socially responsible HRM (SRHRM), organisational citizenship behaviour (OCB), turnover intention, and bank reputation. The proposed model, including seven hypotheses, was examined on a sample of 711 Bangladeshi bank employees. The results suggest that SRHRM has significant positive effects on both OCB and bank reputation, and a significant negative influence on turnover intention. OCB was positively significant for bank reputation but was estimated as insignificant for bank employees’ turnover intention. Moreover, perceived bank reputation was significant and negative on Bangladeshi employees’ turnover intention. Finally, a partial mediation effect was found for OCB on the direct relationship between SRHRM and bank reputation. This paper recommends that banks should aim at higher levels of OCB and reputation and lower turnover intentions should encourage SRHRM in their strategic approaches for HRM and CSR. The implications of the results of this study can help financial organisations to recognise the significance of SRHRM and its favourable effects on employee motivation and institutional reputation.