Our group has been studying a high-temperature superconductor induction/synchronous machine (HTS-ISM). This motor has the same structure as a conventional induction motor. Replacing secondary windings with HTS windings, however, the HTS-ISM has several intrinsic features, i.e., high torque density and high efficiency. In this paper, we established a maximum efficiency control method for the HTS-ISM. This method is based on the electrical equivalent circuit and the optimized excitation condition. We examined the performance of this operation in comparison with the conventional vector control, in which magnetizing current is fixed to be constant. As a result, we found that the HTS-ISM's rotation characteristics were improved by the developed maximum efficiency operation.