This paper presents a variant of the Heckscher-Ohlin model that incorporates multidimensional skill endowment for each agent and team production where team members completely specialize in different tasks, and re-investigates the effects of skill distributions on trade and wages. The equilibrium is characterized by the "effective endowment'', the part of endowment that is actually utilized in production, which depends on the team matches and the task specialization within matched teams. It is shown that: (1) The endowment correlation between skill dimensions for each agent and the skill dispersion across agents, additional to aggregate endowment, both matter for the pattern of trade; (2) Different endowment distributions can also generate different wage inequality levels across countries; An empirically found job polarization pattern can be generated in all developed countries in a global economy; (3) There are new gains from trade, attributed to potential adjustments of the effective endowment upon trade integration. It also reveals a new channel through which institutions may have effects on trade, by shaping the skill distributions. In particular, the potential effects of different educational policies and labor market institutions on skill distributions and trade are discussed.