The work engagement of employees has received increasing attention in the industry and organization psychology literature with the development of “positive psychology”. However, very few empirical studies have addressed the issue in the group level, and no studies examined the effect of supervisor’s engagement on group efficacy. Meanwhile, work engagement is contagious within work groups and may be communicated from supervisor to subordinate, and vice versa. Therefore, this study examines the effect of congruence between supervisor’s work engagement and group engagement climate on group performance. Based on supervisor-group fit theory, we expected that when group supervisors’ work engagement and group engagement climate are in congruence will be have a reinforcement effect on group performance. We also hypothesized that group satisfaction climate had the mediating role on the relationship between supervisor-group engagement fit and group performance. Data were collected from 133 group supervisors and 645 group members using questionnaire survey. The average group size was 4.85(SD = 2.73) with a minimum of three and a maximum of 14 members per group. The group members were asked to complete a questionnaire package assessing group performance, work engagement and job satisfaction. We aggregated the individual-level indices into the group-level variables based on referent-shift consensus model. Their immediate supervisors were asked to rate their work engagement. Theoretical hypotheses were tested by quadratic polynomial regression with response surface technology to analyze the matched sample, and estimated confidence intervals for the linear and nonlinear mediate effects of group satisfaction climate by bootstrapping 20000 samples. The results showed that the levels of group performance will be higher when group supervisors and group members’ engagement are in congruence rather than in dis-congruence. The group performance was maximized in the condition that work engagement between group supervisors and group members are in congruence and high. Meanwhile, group satisfaction climate partly mediated the linear relation between supervisor-group engagement congruent fit and group performance, but didn’t mediate the nonlinear relation between supervisor-group engagement dis-congruent fit and group performance. The present study provided robust evidence for the optimum engagement matching model for group effectiveness by investigating the fit and misfit between group supervisors and group members. Furthermore, this study highlighted the mediating effect of group satisfaction climate, and it expanded the existing literature about the specific mechanism through which group-level process of satisfaction influences group performance. Moreover, it contributes to the literature of work engagement and provided new perspectives for the group-level engagement studies.