This paper formulates a dynamic altruistic model of parental choice of school quality and intergenerational social mobility. It shows that when there are many school qualities, the earnings of children as a function of parental schooling investment is a non-concave function, which leads to multiple steady-state equilibria.The paper studies the intergenerational dynamics of parental schooling investment and gives conditions on the rate of return from parental schooling investment under which some families are stuck in an intergenerational poverty trap. The policy implications are also discussed.