Based on a lever-hinge structure, a target-type fiber Bragg grating (FBG) flow sensor is proposed. Differential measurements of temperature and pressure are achieved using two FBGs. The design idea of the sensor is demonstrated from both theoretical and experimental aspects, and the relationship between FBG wavelength and temperature and the relationship between FBG wavelength and volume flow rate were established, respectively. The sensor is compact with good resolution, high stability, wide measurement range, and easy fabrication, and can be applied to measure temperature and volume flow rate in injection wells.