In this paper, a simpler approach compared to the existing approaches is developed to analyze nuclear reactor dynamics based on the explicit Monte Carlo method. A new population control method is also introduced to prevent neutron population growth and consequent computer memory shortages, which also increases simulation speed. The scheme is applied for time-dependent particle tracking in three-dimensional arbitrary geometries in the presence of feedbacks through a code named MCSP-Explicit. Changes in material density, as well as geometry dimensions, are also considered during simulation. MCSP-Explicit can be run with either continuous or multigroup data libraries, and it is further boosted by parallel processing to speed up simulations. A number of benchmark problems are studied at the end to evaluate the performance of the proposed approach in various situations.