Optimization of a hybrid double-side jet impingement cooling system for high-power light emitting diodes (LEDs) was performed using a hybrid multi-objective evolutionary approach and three-dimensional numerical analysis for steady incompressible laminar flow and conjugate heat transfer using Navier–Stokes equations. For optimization, two design variables, i.e., ratios of the diameter of jet holes and the distance from the exit of upper impinging hole to chips to thickness of substrate were chosen out of the various geometric parameters affecting the performance of the cooling system. To evaluate cooling performance and pressure loss of the system, two objective functions, viz., the ratio of the maximum temperature to average temperature on the chips and pressure coefficient, were selected. Surrogate modeling of the objective functions was performed using response surface approximation. The Pareto-optimal solutions were obtained using a multi-objective evolutionary algorithm, and performances of three representative Pareto-optimal designs were discussed compared to a reference design. In the optimal designs, higher level of uniform cooling was generally achieved with higher pressure coefficient. The Pareto-sensitivity analysis between the objective function and design variable was also performed.