It is essential to use stress-grading systems to suppress corona in the end-turn zone of high voltage machines, which ensure uniform electric field distribution along the end-turn region. Since power dissipation is a major factor in the deterioration process of the grading systems, it is necessary to account for the power loss in the design these systems. This paper presents a novel technique for the design of a linear resistive stress-grading system for high voltage stator winding. This technique is based on minimization of the power loss through the stress-grading system along with equalization of potential along the end-turn zone. A one-dimension lumped circuit model was used and a non-linear constrained optimization algorithm is programmed using MATLAB®. Different discretizations of the grading system are investigated. The lumped circuit model was realized in an experimental setup that confirmed the results of the proposed technique.