Viscous-driven pumping is a very promising type in microscale applications. However, there exist a few disadvantages such as low efficiency and small volume flow rate. In the present study, a pump with tandem rotating cylinders and its optimum synthesis are proposed fur enhancing pumping performance. First, using an unstructured grid CFD method, we investigate the effects of geometrical parameters and then the performance of the pump with tandem cylinders is evaluated. Next, an optimum design synthesis tool is constructed by combining the aforementioned CFD analysis model with the mathematical optimization model, namely, Modified Method of Feasible Directions (MMFD). This technique is used to optimize the geometrical parameters of the pump, fur maximizing pumping efficiency. From the optimization results, it is believed that the present optimum synthesis is robust and has a potential fur other microfluidic device design.