The paper is dedicated to the study and the optimization of a magnetohydrodynamic conduction pump. Electromagnetic pumps have several advantages to mechanical pumps, they do not use a moving mechanical part, unlike traditional electric motors, and they transform electromagnetic energy directly into kinetic energy. A fluid is set in motion in a magnetic field by an electric field supplying an electric current to the terminals of electrodes immersed in the fluid. The optimization procedure based on the particle swarm method uses a fitness function as the minimum of the mass. The electromagnetic model is carried out by the finite volume method and the steady fluid flow by COMSOL software. The optimized results of the performance characteristics of the electromagnetic pump are obtained.