Concrete-cored sand–gravel piles are a kind of composite pile formed by wrapping a concrete-cored pile with a sand–gravel shell, which has the advantages of both a rigid pile and bulk-material pile. The bearing characteristics of the concrete-cored sand–gravel pile composite foundation were investigated by establishing a three-dimensional discrete element numerical model for a cyclic dynamic loading test. The results show that the vertical stress of the core pile body fluctuates greatly at the beginning of loading, and the fluctuation amplitude decreases with the depth, and gradually tends to be stable in the middle and late stages, and the vertical-stress distribution is relatively uniform. The radial stress in the upper part of the core pile body fluctuates greatly, the fluctuation in the lower part is small, and the radial stress in each part of the core pile body gradually tends to be stable in the late-loading period. The radial stress factor of the core pile body reaches the stable speed with the foundation depth decreasing; the fluctuation amplitude of the pile-soil stress ratio decreases with the foundation depth and gradually tends to be stable with the increase in loading. The results of this study can provide a reference for the design and construction of a core sand pile composite foundation.