The purpose of this paper is to investigate what are the investments for fiscal policy relating to education to achieve the second best within a framework of a two-period overlapping generations model where the human capital of children is accumulated through the education investment by parents. Especially, we focus on the subsidy for (tax on) education investment with different population growth rate. We show that (i) whether the government subsidizes for (taxes on) the education investment basically depends on the configuration of the marginal productivity of human capital and that of physical capital. When the individuals do not strongly prefer the human capital of their children and the human capital is under-accumulated, then the government always subsidizes for the education investment, (ii) If the population growth rate is high, the level of subsidy rate for the education investment of the government is low.