A motor drive system capable of suppressing heat generation during a low speed operation may include: an inverter including a plurality of switching elements to convert direct current power to alternating current power having a plurality of phases; a motor driven with the alternating current power converted in the inverter; and a controller determines an operating point of the motor on the basis of a torque command of the motor and generates a d-axis current command and a q-axis current command corresponding to the operating point. In particular, when each of the switching elements is overheated, the controller changes the d-axis current command and the q-axis current command by changing the operating point to a different operating point corresponding to a torque of the same magnitude as the torque command.