Centrifugal pumps are the critical components in deep-sea mining. In order to investigate the particle motion in the curved channel of the impeller, three different types of curvature conform to blade profile to simplify the impeller design of pumps. A numerical study is conducted to investigate the flow field in a varying-curvature channel for solid-liquid two-phase flow. The flow of particles within the varying curvature channel is studied by combining the discrete element method (DEM) with computational fluid dynamics (CFD) and a comparison with Particle Image Velocimetry (PIV) test results. The results show that a polyhedral mesh with a small mesh number yields very accurate results, which makes it very suitable for CFD-DEM. Based on this method, the movement of a single particle is compared and analyzed, and the particle-motion law is obtained. The effects of the curvature ratio Cr and area ratio Ar on the motion law for a single particle are studied, and the simulation results are analyzed statistically. The results show that the effect of Cr on both the particle slip velocity and the turbulent kinetic energy only changes its strength, while the distribution law does not change significantly. Compared with the curvature ratio Cr, the area ratio Ar has a greater impact on the particles, and its distribution law becomes clearly different. As the area ratio Ar increases, the arc radius and length of the corresponding particle trajectory decrease.