This paper proposes a new and advanced methodology for finding the optimum electrical design of high voltage ac capacitive graded bushings using an improved genetic algorithm approach as an effective meta-heuristic method. A case study has been conducted on a 145 kV oil impregnated paper (OIP) bushing and the IEC 60137 tests have been performed to evaluate its performance. Condenser-bushings contain concentric conductive foils which are isolated from each other. The partial capacitances between conducting cylinders can be modified by adjusting the number, diameter, place and length of these cylinders as well as the thickness of insulating material between foils. As a result, the voltage drop and also the electrical stress in the core and along the surface will change. This paper finds optimal value of bushing design parameters to achieve well-distributed electric stress with the lowest possible maximum value and also a constant voltage drop for different layers by using an improved genetic algorithm optimization method subject to practical and technological constrains. The proposed method of this research work has been applied to a 145 kV OIP bushing. The performance of optimal designed 145 kV OIP bushing under IEC 60137 tests is very promising.