The electrical contact resistance greatly influences the thermal behavior of substation connectors and other electrical equipment. During the design stage of such electrical devices, it is essential to accurately predict the contact resistance to achieve an optimal thermal behavior, thus ensuring contact stability and extended service life. This paper develops a genetic algorithm (GA) approach to determine the optimal values of the parameters of a fractal model of rough surfaces to accurately predict the measured value of the surface roughness. This GA-optimized fractal model provides an accurate prediction of the contact resistance when the electrical and mechanical properties of the contacting materials, surface roughness, contact pressure, and apparent area of contact are known. Experimental results corroborate the usefulness and accuracy of the proposed approach. Although the proposed model has been validated for substation connectors, it can also be applied in the design stage of many other electrical equipments.