The development of a parallel three-dimensional direct simulation Monte Carlo (DSMC) method using unstructured cells is reported. Variable hard sphere molecular model and no time counter method are used for the molecular collision kinetics, while the cell-by-cell ray-tracing technique is implemented for particle movement. Developed serial code has been verified by comparing the results of a supersonic corner flow with those of Bird's three-dimensional structured DSMC code. In addition, a benchmark test is performed for an orifice expanding flow to verify the parallel implementation of DSMC method by comparing with available experimental data. Static physical domain decomposition is used to distribute the workload among multiple processors by considering the estimated particle weighting distribution. Two-step multi-level graph partitioning technique is used to perform the required domain decomposition. Completed code is then applied to compute a hypersonic flow over a sphere (external flow) and the flow field of a spiral drag pump (internal flow), respectively. Results of the former are in good agreement with previous numerical results using axisymmetric DSMC method and experimental data. Results of the latter also agree well with previous numerical results.