Abstract: In order to deal with the effect that fertility rate fluctuation brings with pay-as-you-go pension system, with the introduction of education financing and capital flow, considering the fertility rate under the condition of random fluctuations fixed benefit payment rate and fixed contrbution rate various combinations of pension system, to find a pay-as-you-go pension system sustainable running the best adjustment scheme. This paper extends the three-period computable general equilibrium model, and explores the impact of fertility fluctuations on pension system design under different degrees of capital mobility based on a given education system. The results show that defined-benefit pension systems are more popular than defined-contribution pension systems for closed economies with low capital mobility. However, for an open economy with high capital mobility, if the education system has a fixed benefit rate, the fixed contribution rate pension system is more popular than the fixed benefit rate pension system, and in this case, the choice of pension system is not affected by fertility fluctuations.