In this paper, a numerical study has been performed to investigate the effect of geometrical parameters of a viscous micro-pump on the flow rate and entropy generation. The present research has been carried out for three geometrical parameters of micro-pump including eccentricity (), sizes (S) of rotors and also their distance from each other (L) in the range of 0.1 to 0.9, 1.5 to 3.5 and 0.85 to 4.5, respectively. The results show that with increasing , the micro-pump flow rate also increases. On size variation effects, it is observed that decreasing the downstream rotor diameter, while keeping constant the upstream rotor diameter, the flow rate decreases exponentially. By increasing L, a steep increase in flow rate is initially observed, which becomes almost constant, when rotors are sufficiently far apart. With regard to entropy analysis, the effect of above geometrical parameters has been investigated on the entropy generation. The parameter RS indicating the ratio of the gradient of the entropy production rate to the related flow rate is introduced as a tool for entropy analysis. Also in this paper, for obtaining the maximum flow rate at the minimum frictional dissipation, optimal geometrical parameters are extracted. In this regard, the values of L=2, ε=0.5, S_1=1.5 and S_2=2.5 are selected as the optimum geometrical parameters of viscous micro-pump.