© 2021 Elsevier LtdThe kinetic population balance model (PBM) is widely used to predict the particle size distributions of ball milling products. The matrix model can be easily used for the same purpose if the grinding time can be incorporated into the relevant model. This study proposes and demonstrates an accurate algorithm that uses a pseudo-matrix model to simulate the product size distributions (PSDs) of successive breakage events in batch grinding. The simulation results indicate that the breakage events in the mills may be determined by attraction forces between particles and grinding media. The algorithm is shown to be widely applicable to different combinations of samples and grinding equipment. The algorithm can even work with arbitrary sets of parameters that are irrelevant to the mill feed. Therefore, the proposed algorithm with its mathematical framework may be fundamental to different size reduction methods. Also, the algorithm is shown to have a potential for predicting the product PSDs of continuous milling.