We report a novel fiber-optic anemometer with self-temperature compensation capability based on a Fabry-Perot interferometer (FPI) formed by a thin silicon film attached to the end face of a single-mode fiber. Guided in the fiber are a visible laser beam from a 635 nm diode laser used to heat the FPI and a white-light in the infrared wavelength range as the signal light to interrogate the optical length of the FPI. Cooling effects on the heated sensor head by wind is converted to a wavelength blueshift of the reflection spectral fringes of the FPI. Self-temperature-compensated measurement of wind speed is achieved by recording the difference in fringe wavelengths when the heating laser is turned on and then off. Large thermal-optic coefficient and thermal expansion coefficient of silicon render a high sensitivity that can also be easily tuned by altering the heating laser power. Furthermore, the large thermal diffusivity and the small mass of the thin silicon film endow a fast sensor response.