A novel flow velocity sensor based on fiber grating by using the fiber grating pressure sensing setup and Venturi tube is designed. The expression of relationship between the flow velocity and the shift of central wavelength of fiber grating is derived and the experimental results are in good agreement with theoretical analysis. The central wavelength of fiber grating shifts to the shorter wavelength with rise of the flow velocity, while the bandwidth is almost unchanged. The sensor is very sensible to the flow velocity, and very stable. The measuring range is 51.0～148.2 mm/s and in that range the sensor can distinguish the change of the flow velocity as low as 0.3 mm/s which is the lowest to our knowledge. By optimizing the parameters of the sensor, the sensitivity can be improved and it can measure the velocity of different ranges.