In the present paper a numerical simulation based on the LBM is performed to analyze a viscous micropump with a single elliptic rotor. The effects of three important geometric parameters including aspect ratio of rotor, micropump height and rotor eccentricity are investigated on the average flow rate and entropy generation. The obtained results from the simulations are analyzed by response surface method (RSM). The results indicate that the average flow rate increases by increasing the aspect ratio and rotor eccentricity and decreases by increasing the micropump height. Moreover, the sensitivity of the average flow rate to changes of aspect ratio and eccentricity is more than the change of microchannel height. The results also show that by increasing all three geometric parameters, the average entropy generation increases and is sensitive to changes of three geometric parameters. Finally, the optimal geometric parameters are determined by RSM that for maximizing the flow rate, the optimum values of 1, 1.5 and 0.9 are for aspect ratio, height and eccentricity respectively and for minimizing the entropy generation, the optimum values of 0.2, 1.5 and 0.1 are achieved.