In this paper, we propose an analytically tractable overlapping-generations model of human capital accumulation and study its implications for the evolution of the US wage distribution from 1970 to 2000. The key feature of the model, and the only source of heterogeneity, is that individuals differ in their ability to accumulate human capital. Therefore, wage inequality results only from differences in human capital accumulation. We examine the response of this model to skill-biased technical change (SBTC) theoretically. We show that in response to SBTC, the model generates behavior consistent with some prominent trends observed in the US data including (i) a rise in overall wage inequality both in the short run and long run, (ii) an initial fall in the education premium followed by a strong recovery, leading to a higher premium in the long run, (iii) the fact that most of this fall and rise takes place among younger workers, (iv) a rise in within-group inequality, (v) stagnation in median wage growth (and a slowdown in aggregate labor productivity), and (vi) a rise in consumption inequality that is much smaller than the rise in wage inequality. These results suggest that the heterogeneity in the ability to accumulate human capital is an important feature for understanding the effects of SBTC and interpreting the transformation of the US labor markets since the 1970s.