This study investigates how leadership, more precisely leader–member exchange (LMX), affects innovative behavior through an innovative climate as well as, indirectly, through organizational commitment and internal trust. A total of 1114 samples were collected from employees working in firms in Slovenia and Serbia. The quantitative data and the proposed model were analyzed with the partial least squares—SEM technique. The results indicate that an innovative climate is a mediator in the relationship between leadership and innovative behavior, and this relationship is also further mediated by internal trust and organizational commitment. These results reveal serial mediation or the complex role of an innovative climate in the process of influencing innovative work behavior. Implications for theory and recommendations for practice are discussed.