The importance of citizen deliberation in democracy is widely recognized today and the current digitalized and more fragmented society may benefit from discussions among people with diverse opinions in a well-organized setting. At the same time, concerns have also been raised about inequality in deliberative participation. We narrowed our focus to gender equality and examined whether introducing an evidence-driven style of deliberation can mitigate gender inequality in policy deliberation. In our repeated measure (within-subjects) experiment, university students in Japan discussed divisive policy issues during two sessions. Half of the participants started the discussion by examining factual information about the topic (evidence-driven style) and the other half started the discussion by expressing opinions about the topic (verdict-driven style). In the second session, the two groups switched styles. We found a statistically significant gender gap in participatory contribution for the verdict-driven style, but no such gap existed for the evidence-driven style. Using causal mediation analysis, we also found that, compared with the verdict-driven style, the evidence-driven style of deliberation reduces the gender gap by lowering women's tendency to agree with men. One possible explanation from the viewpoint of gendered communication is that women were more confident in evidence-driven deliberations. This psychological effect is a factor that is harder for facilitators to control and thus the evidence-driven style can be effective even with the presence of facilitators. This paper demonstrates the importance of studying how deliberations are conducted and how deliberation styles can affect the content and the consequences of policy deliberations.