Optical switches based on phase change materials have enormous application potential in optical logic circuits and optical communication systems. Integration of all-optical switching devices with optical fibers is a promising approach for realizing practical applications in enabling the optical fiber to transmit and process signals simultaneously. We describe an all-fiber nonvolatile broadband optical switch using an all-optical method. We use a single optical pulse to modulate the phase change material deposited on the tapered fiber to achieve logical control of the transmitted light. The response time of our optical switch is 80 ns for SET and 200 ns for RESET. Our optical switches can operate in the C-band (1530-1565 nm). The optical switching contrast is 40%. Our approach paves the way for all-optical nonvolatile fiber optic communication.