Many studies examine how public school education and private school education affect human capital accumulation. Public school education is financed by taxation, but private school education is financed by households. Here, we construct a human capital accumulation model incorporating school education and private supplementary tutoring, and examine how private supplementary tutoring affects human capital accumulation. Our results demonstrate that private tutoring leads to inequality of human capital accumulation in the case of public school education. Moreover, we show that if public school education is complementary with private supplementary tutoring, low-income households are unable to choose public school education because of private supplementary tutoring costs. Therefore, public school education is not appropriate as a redistribution policy to benefit low-income households.