Previous research has merely explored the positive relationship between cognitive diversity and creativity, but the potential negative side of cognitive diversity might also prevail and should be examined together with its positive side. To address this gap, our study, drawing on the categorization–elaboration model framework, explored both the positive and negative effects of cognitive diversity on creativity/innovation in a single model. Using data collected from 101 teams (including both team leaders and team members) in 10 Chinese manufacturing companies, we identified a dual pathway – namely, task reflexivity (i.e., positive pathway) and relationship conflict (i.e., negative pathway) – in the linkage of cognitive diversity and innovative work behaviour (i.e., IWB). Cognitive diversity encouraged IWB via the task reflexivity pathway, but impeded IWB via the relationship conflict pathway. We further demonstrated that perceived support for innovation moderated the relationships between cognitive diversity and task reflexivity/relationship conflict, with cognitive diversity more related to task reflexivity and less related to relationship conflict when perceived support for innovation was high. Moderated mediation effects also indicated that the positive indirect effect of cognitive diversity on IWB through task reflexivity existed only when support for innovation was high and that the negative indirect effect of cognitive diversity on IWB through relationship conflict occurred only when support for innovation was low.