In this paper, a 3D model of magnetohydrodynamic (MHD) micropump with a rectangular channel was modeled and numerically simulated based on the finite volume method. Effects of geometrical parameters such as depth, width, and length of the side electrodes were studied on the maximum flow rate, maximum pressure, and energy rate of the rectangular MHD channels in constant electric current and constant power supply modes. The multiple attributes decision-making method was used in order to identify the most effective geometrical parameters on the performance of the micropump. Wider channels with long electrodes are identified to be in favor of high performance for high flow rate, high pressure, and energy-efficient demands. A case study of new profile with a widened channel in the pumping section was proposed, and its new geometrical parameters are introduced. Studies at constant energy rate of 1 mW showed that the extension of the channel width (electrode walls) can increase the flow rate up to 1.23 μl/min (34% increase in comparison with non-extended channel). Additionally, it was found that when the extension parameter is set to 3.5 (D/w = 3.5), the flow rate is independent of the elongation parameter (r/R).