Abstract With the progress of computing ability, so far the three-dimensional motion of particles has been simulated more accurately. It often spent lots of time on simulating huge amount of particles due to contact detection. In this paper, a three-dimensional ball theory based on Discrete Element Method(DEM) original proposed by Cundall(1971) was developed, the concept of accelerated search was introduced, and the contact detection was simplified to increase the efficiency of programs. Furthermore, because there was no standard about time step and the range of contact spring stiffness in the past, the purpose of this paper is to set up a relation to the selection of parameters and organized into a chart by a series of simulation tests. Users can select the required parameters individually according to the chart in the future. Under the premise of reasonable and credible simulations, this paper also discuss the concept of critical velocity to derive the upper limit of ball velocity on normal contact in order to avoid errors.