Abstract Heat exchangers are widely used in the industry to allow the heat transfer between two fluids. For that reason, correctly sizing said devices poses a design problem in order to guarantee the efficiency and appropriate conditions of the equipment and the processes. In this paper, the geometry of a spiral-plate heat exchanger is optimized by means of a particle swarm optimization algorithm, whose objective function is the maximization of the overall heat transfer coefficient. The process variables considered in the model were channel spacing, spiral length, spiral width, and wall thickness. The mathematical model and the particle swarm optimization were programmed in Matlab®, where the parameters and the constraints were defined, limiting the pressure drop and guaranteeing the heat transfer required for a study case taken from Minton’s work. In this study, the overall heat transfer coefficient was increased by 12.73% in comparison with the original design.