In this study, seven groups of three-dimensional finite differential numerical simulation tests were performed to investigate the dynamic characteristics of the composite foundations of geogrid-encased piles under cyclic loading. The effects of four important parameters on the behavior of the encased piles were evaluated. The numerical calculation results are compared with those of laboratory model tests, which verifies the rationality of the numerical results. The results show that the stress and settlement of encased stone piles composite foundations have obvious dynamic characteristics under cyclic loading. Under the same cyclic loading condition, increasing the gravel density could effectively improve the bearing capacity of the piles. The encasement can improve the mechanical properties of the piles, and the encasements with different lengths have different effects on the piles. Increasing the encasement length in a certain range can effectively improve the bearing capacity of the stone piles. The encasement has a significant effect on the cumulative settlement and stress concentration at the top of composite foundations. The encasement can improve the integrity of the stone piles, and increasing reinforcement length can lead to better vibration coordination of the stone piles. Pile diameter has an obvious influence on the cumulative settlement at the top of encased stone pile composite foundations, and the optimal L/d value of the stone pile is 8/3. The results of numerical calculation fit well with those of laboratory model tests. The maximum difference in settlement value is 7%, and the maximum difference in lateral stress of the pile is 9%.