Motivated by increasing trade and fragmentation of production across countries since World War II, we build a dynamic two-country model featuring sequential, multi-stage production and capital accumulation. As trade costs decline over time, global-value-chain (GVC) trade expands across countries, particularly more in the faster growing country, consistent with the empirical pattern. The presence of GVC trade boosts capital accumulation and economic growth and magnifies dynamic gains from trade. At the same time, endogenous capital accumulation shapes comparative advantage across countries, impacting the dynamics of GVC trade: a country becoming more capital abundant concentrates more on the capital-intensive stage of the production.