This paper presents a design study on a 40 MW synchronous motor having no-insulation (NI) high-temperature superconductor (HTS) field coils. An in-house analytic code was used to obtain a first-cut design based on the published parameters of the AMSC 36.5 MW ship propulsion motor as a reference. Then, design refinement was followed using the finite-element method to more accurately simulate electromechanical behaviors of the motor. After the final design was completed, transient torque responses of the NI motor, in no load and full load conditions, were simulated with our new equivalent circuit model to consider the nonlinear behaviors of the NI field coils, and compared the results with those of its insulated counterpart. The overall torque response of the NI machine was essentially identical to that of the insulated one, though a notable discrepancy was observed at the moment when the rotor acceleration started and ended. The results may imply that the NI field coils play a role as an effective damper in perspective of the torque response. The results demonstrate a potential to use the NI HTS field coils for a low-speed synchronous machine such as the ship propulsion motor.