When lunar probes make a landing on the lunar surface, lunar-soil particles will be blown away by the engine plume with a significant collision phenomenon. The hard-sphere model, whose governing equations satisfy the momentum and kinetic-energy conservation equations, is used in research to study collision phenomena among particles having different diameters. The lunar-soil particles with different diameters collide 36.8-153.2 times on average, and the average speed is 50.4-426.7 m/s assuming no energy loss. When the recovery coefficient is reduced from 1.0 to 0.1, the average number of collisions increases by 16.3%-65.7%, and the average speed decreases by 24.2%-49.8%. Furthermore, the number of particle-occupied space grids increases for small-diameter lunar-soil particles as the collision process loses energy but decreases for large-diameter particles. Overall, the collision phenomenon among lunar-soil particles under engine plumes is important because it causes massive momentum and kinetic energy transfers among particles, which alters particle spatial trajectory and distribution.