Effects of the Reynolds and Knudsen numbers on a micro-viscous pump are studied by using a Navier-Stokes code based on a finite volume method. The micro viscous pump consists of a circular rotor and a two-dimensional channel. The channel walls are treated by using a slip velocity model. The Reynolds number is studied in the range of $0.1{sim}50$. The Knudsen number varies from 0.01 to 0.1. Numerical solutions show that the pump works efficiently when two counter rotating vortices formed on both sides of the rotor have the same size and intensity. As the Reynolds number increases, the size and intensity of the vortex on the inlet side of the pump decrease. It disappears when the Reynolds number is larger than about Re=20. The characteristics of the performance of the pump is shown to deteriorate, in terms of mean velocity and pressure rise, as the Reynolds number increases. The Knudsen number shows a different effect on the characteristics of the pump. As it increases, the mean velocity and pressure rise decrease but the characteristics of the vortex flow remains unchanged, unlike the effect of Reynolds number.