Abstract: The organic materials used in spacecraft may outgas under the space environment, including, mainly, the vacuum, the high & low temperature, and the influence of the ionization irradiation. The outgassing product has harmful effects on the spacecraft itself. So a quantitative assessment of the contamination effects is necessary. The molecular transport process is modeled by the Monte-Carlo method, with the rays representing the molecule trajectories, to simulate the motion process of a large number of molecules. Thus the transport process is transformed into a ray tracing problem. Due to the complexity of the spacecraft configurations, the ray tracing computation might be very time consuming, therefore, it is extremely necessary to have an accelerating algorithm. In this paper, the complex geometry of the spacecraft surface is modeled with triangular unstructured grids, the octa-tree space subdivision technology is used to accelerate the molecular motion and surface intersection calculations. At the same time, based on the shared memory multi-core computing platform, the OpenMP API is used to implement parallel computing for the simulation. The test case shows a significant acceleration in the calculation, and the developed method is applied to the contamination analysis of a space station.