Purpose Prior studies have consistently shown that leader psychological capital is beneficial for leader–member exchange (LMX) and followers’ outcomes. In this study, the authors challenge this consensus; they propose that a leader with high-level psychological capital may decrease LMX and promote followers’ turnover intention when encountering a follower with low-level psychological capital. Only congruent psychological capital in leader–follower dyads increases LMX and decreases turnover intention.Design/methodology/approach A two-wave survey was designed to collect data from a sample of 207 leader–follower dyads in the service industries of China. Polynomial regression combined with the response surface analysis was used to test the hypotheses.Findings (1) LMX increased when the levels of psychological capital between leaders and followers were congruent, but LMX suffered when they were not congruent (e.g. leaders’ psychological capital was higher than followers’ or otherwise); (2) in the conditions of psychological capital congruence, LMX was higher when a leader’s and a follower’s psychological capital were both high than low; (3) LMX mediated the relationship between psychological capital congruence and followers’ turnover intention.Originality/value These findings provide a novel perspective on understanding of the function of psychological capital and its implications for turnover management.