The linear mercury diffusion pump is proposed as the primary pump for sustaining the continuous working of KALPUREX (Karlsruhe liquid metal based pumping process for fusion reactor exhaust gases), which is considered as the exhaust pumping solution for reducing the tritium inventory in future fusion reactor with the fuel cycle based on the Direct Internal Recycling (DIR) concept. In this work, a preliminary simulation study of the linear mercury diffusion pump (LDP) is performed based on the Direct Simulation Monte Carlo (DSMC) method. While the dsmcFoam solver in the OpenFOAM platform is used, the inlet model named by fixed mass-flow-rate (FixedMFR) model is developed to control the mass flow rate into the pump, in accord with the condition of the experiment in 1950s. The simulated pumping speeds are in reasonable agreement with the experimental results when the pressure is in the range of 1 × 10−2 ~ 2 × 10−2 Pa, which implies that the DSMC model can be used for simulating the performance of the LDP. It should be noted that in the preliminary DSMC model, the mesh size is too large. Due to the large mesh size, the expansion of the mercury vapor steam is overestimated and the pumping speed is underestimated. Further work is required to find a proper way to generate the computational mesh for predicting the pumping performance of the LDP accurately and effectively.