A fiber-optic anemometer based on fiber Bragg gratings (FBGs) is presented. A short section of cobalt-doped fiber was utilized to make a fiber-based "hot wire" for wind speed measurement. Fiber Bragg gratings (FBGs) were fabricated in the cobalt-doped fiber using 193 nm laser pulses to serve as localized temperature sensors. A miniature all-optical fiber anemometer is constructed by using two FBGs to determine the dynamic thermal equilibrium between the laser heating and air flow cooling through monitoring the FBGs' central wavelengths. It was demonstrated that the sensitivity of the sensor can be adjusted through the power of pump laser or the coating on the FBG. Experimental results reveal that the proposed FBG-based anemometer exhibits very good performance for wind speed measurement. The resolution of the FBG-based anemometer is about 0.012 m/s for wind speed range between 2.0 m/s and 8.0 m/s.