This paper develops an endogenous growth model with technological knowledge directed towards high- versus low-skilled labour, augmented with North–South international trade of intermediate goods and with human-capital accumulation, to analyse how trade affects wage inequality and the inter-country human-capital gap. Trade is a vehicle for inter-country technological-knowledge diffusion and human-capital accumulation interacts with the intra-country direction of technological knowledge arising from trade. In contrast with the market-size effect, stressed in the skill-biased technological change literature, the operation of the price channel following openness to trade predicts, in line with the recent trends in developed and developing countries, an increasing technological-knowledge bias towards high-skilled human capital. This, in turn, decreases inter-country gaps of technological knowledge and human capital and increases intra-country wage inequality. Also in line with recent empirical evidence, inter-country wage convergence is induced by the trade-opening level effect.