An apparatus and method for driving a 2-phase SRM are provided. The method may include initializing 2-phase SRM based on a detected position of a rotor by an initializing sensor at a time of an initial driving, and normally driving the 2-phase SRM based on a detected position of the rotor by a driving sensor. With this method, a sufficient amount of torque is generated when the 2-phase SRM is driven at a high speed. The apparatus may include an initializing sensor that detects each position of each phase of a 2-phase SRM, and generates an initializing sensor signal based on the detected result; a driving sensor that detects each position of each phase of the 2-phase SRM, and generates a driving sensor signal based on the detected result; and a microprocessor that initially drives the 2-phase SRM based on the initializing sensor signal at the time of an initial driving, and normally drives the 2-phase SRM based on the driving sensor signal at the time of a normal driving.