The objective of this study was to solve the theoretically ideal arm stroke for a swimmer with hemiplegia by using the optimizing simulation. The method of optimizing simulation for non-disabled swimmers was extended to a swimmer with hemiplegia. In order to evaluate the arm strokes in the optimizing calculation, the swimming human simulation model SWUM was employed. As the design variables, the joint angles in the three time frames, in which the arm was performing underwater strokes, were used. The objective function was the swimming speed. Three constraint conditions including the maximum joint torque characteristics were imposed on the optimizing calculation. The swimming motion of an actual swimmer with hemiplegia was measured and put into the simulation as the original motion. In the simulation, significant increase in the swimming speed was obtained in the case of the optimized stroke with the actual swimmer's wrist motion at the slower stroke cycle. From the comparison between the optimized stroke and the actual swimmer's stroke, several differences were found as follows. First, at the entry phase in the fastest optimized stroke, the left elbow was more extended than the actual swimmer's stroke. Second, at the catch phase in the fastest optimized stroke, the forearm in the side view was more tilted with respect to the vertical line, while that in the actual swimmer was almost vertical. Third, at the pull and finish phases in the optimized stroke, the hand pushed the water sufficiently to the end, while that in the actual swimmer went out from the water earlier. Overall, it was found that the optimized stroke effectively utilized the joint torque at the shoulder and elbow to the maximum extent, by selecting the more natural positions and the slower stroke cycle.