Navier-Stokes simulation of the flow in a micro viscous pump is carried out. The micro viscous pump consists of a rotating circular rotor placed in a two dimensional channel. All simulation is carried out by using a finite volume approach, at the Reynolds number of 0.5, to study the performance of the micro viscous pump. Length of channel of the pump is varied to simulate the effects of the pumping load. Numerical solutions show that the net flow of the pump is realized by two counter rotating vortices formed on both sides of the rotor. The volume flow rate of the pump is decreased as length of the channel is increased, while the static pressure difference across the rotor is increased. The static pressure difference across the rotor is observed to be inversely proportional to the volume flow rate as inertia effects are negligibly small. The efficiency of the pump is found to reach a maximum when two counter rotating vortices on both sides of the rotor becomes to merge forming an outer enveloping vortex.