Team psychological capital (Team PsyCap) is a valuable team resource beyond individual psychological capital. From the perspective of team interaction process, this paper examines how Team PsyCap exerts different effects on the two types of team processes—team integration process and team differentiation process, and consequently affects team task performance and individual task performance. The empirical results show that: (1) Team PsyCap positively affects team task performance and individual task performance; (2) Team PsyCap can promote team collaboration and reduce team conflicts; (3) Team collaboration and team conflict mediate the relationship between Team PsyCap and team and individual performance respectively.