The direct simulation Monte Carlo Method is applied to investigate the two-dimensional flow fields of a turbomolecular pump(TMP) in both molecular and transition flow regions. The pumping characteristics of the TMP are investigated for a wide range of the Knudsen number. The maximum of compression ratio and of pumping speed strongly depend on the Knudsen number in transition region, while they weakly depend on the Knudsen number in free molecular flow region. The present numerical results show good agreement with the previously known experimental data. Finally. the results of the single blade row in both molecular and transition regions are used to predict the overall performance of a TMP, which has three kinds of blade with 24-rows.