A novel fiber magnetic sensor based on the fiber Bragg grating Fabry-Perot (FBG-FP) cavity ring-down technique with pulse laser injection is proposed and demonstrated theoretically. A general expression of the intensity of the output electric field is derived, and the effect of the external magnetic field on the ring-down time is discussed. The results show that the output light intensity and the ring-down time of the FBG-FP cavity are in the inverse proportion to the magnitude of the external magnetic field. Our results demonstrate the new concept of the fiber magnetic sensor with the FBG-FP cavity ring-down spectroscopy and the technical feasibility.