A novel fiber anemometer based on two pairs of fiber gratings is experimentally demonstrated and can simultaneously detect wind speed and wind direction. One pair of gratings, which are separated by 90° in space, is fixed on a small stainless steel pipe driven by a rotating disc for measuring the wind-direction angle. The other pair is composed of a sensing and a matched grating. The frequency of the spectrum-shifted of the sensing grating to overlap with that of the matched grating is employed for determining the wind speed. The errors in the wind-speed and wind-angle measurements are experimentally demonstrated to be less than 1%. The proposed fiber anemometer with a simple and durable structure can be applied in wind-powered electricity generators.