This paper presents a numerical analysis of a novel configuration of Knudsen pump for rarefied gas flow. The pumping element consists of two facing isothermal ratchet surfaces at different temperatures. The asymmetric saw-tooth-like surfaces in optimal geometrical conditions can create temperature inequalities in the near wall region and finally engender a macroscopic flow. The rarefied gas flow is numerically investigated by Direct Simulation Monte Carlo (DSMC) in the slip and transition regimes. A parametric study reveals the effects of several crucial parameters including temperature difference, Knudsen number, accommodation coefficients as well as main geometrical parameters. In particular, the results indicate that the mass flow rate reaches a maximum value for a Knudsen number around 0.1 and becomes negative for a Knudsen number close to unity.