In this paper, a novel distributed optical fiber temperature sensor based on Raman anti-Stokes scattering light is proposed and experimentally demonstrated. The Raman anti-Stokes scattering light is sensitive to temperature parameters that are detected by the fiber under test conditions (FUT), and this allowed the temperature demodulation algorithm to be obtained through the relationship between the temperature and the power of the back-scattered Raman anti-Stokes light. In addition, we propose a new temperature calibration method to ensure accurate temperature measurement, which is greatly affected by the stability of a pulse laser. The experimental system is constructed with an optical fiber length of approximately 3.5 km. The proposed system obtains a 24 dB dynamic range with a pulse width of 20 ns and temperature testing ranges of 30.0 °C to 80.0 °C. The results demonstrate that the maximum temperature deviation range is −1.5 °C to +1.6 °C and the root mean square (RMS) error of the whole temperature range is 0.3 °C, which means it has the potential for practical engineering applications. More importantly, it avoids the walk-off effect that must be corrected in commonly used temperature demodulation schemes adopting both Raman Stokes light and anti-Stokes light. It also saves a signal channel, which is more suitable for the integration of hybrid distributed optical fiber sensing systems for multi-parameter monitoring.