Purpose The purpose of this paper is to investigate the effects of empowering leadership, directive leadership and initiating structure on innovation in small and medium enterprises (SMEs) and examine the mediating role of climate for innovation on those relationships. Design/methodology/approach Applying structural equation modeling, the study empirically tested the model on a sample of 330 employees from tourism SMEs in Vietnam. Findings Results indicated that climate for innovation mediated the relationship between empowering leadership and innovation and also initiating structure and innovation. Whereas empowering leadership was found to have a negative direct influence on innovation, directive leadership was unrelated to innovation. Research limitations/implications - The results of this study contribute to the literature by expanding the existing research on SME innovation, assessing the effect of diverse leadership styles and a climate for innovation on the innovation performance of SMEs. The findings enrich the literature by indicating the contribution of empowering leadership, directive leadership and initiating structure on encouraging innovation in SMEs. Practical implications - When leading subordinates in the SME context, leaders who have a clear understanding of the effect of empowerment, direction and initiating structure can optimally seek to stimulate innovation. These leadership approaches influence employees' task, interpersonal and role-related processes that shape a climate for innovation. Originality/value The novelty of this paper is that it examines the differential influences of empowering leadership, directive leadership and initiating structure on innovation and the mediating role of climate for innovation on these relationships.