Team psychological safety — a non-threatening and safe climate — allows team members to express and share each other's opinions freely, and this sharing may produce more useful perspectives to induce team creativity. In a psychologically safe climate, transactive memory systems (TMSs) may be constructed for describing the specialised division of cognitive labour for solving information problems and thereby enabling team members to quickly gain and use knowledge across domains. As a consequence, further ideas may be generated within teams, increasing team creativity. Our research model is assessed using data from a sample of 110 team members from 40 research and development (R&D) teams in a leading technology company in Taiwan and analysed using the partial least squares method. The results of this study reveal that: (1) team psychological safety did not directly affect team creativity, (2) team psychological safety affects TMSs, (3) TMSs affect team creativity, and (4) TMSs fully mediate the relationship between team psychological safety and team creativity. This study also discusses the implications for team creativity.