In a system for driving a brushless motor having motor drive coils connected to respective drive transistors, voltages induced in the drive coils when the motor is rotating are continuously detected to produce energization switching signals to be applied to the drive transistors, thereby switching over energization of the drive coils, so that the motor can be continuously driven at optimum energization timing regardless of its rotational speed. Further, when a rotational direction command signal is applied to a forward-backward switching circuit to instruct the motor to rotate in the backward rotational direction while the motor is rotating in the forward rotational direction, torque of the opposite direction is produced to change the rotational direction of the motor. Further, separate-excitation timing pulse signals are used to sequentially switch over energization of the motor drive coils when the motor is not rotating or it is rotating at a very low speed, and hence voltages induced in the motor drive coils cannot be detected. As soon as the voltages induced in the drive coils have become able to be detected due to the rotation of the motor, self-excitation timing pulse signals are then used to sequentially switch over energization of the drive coils.