The optical fiber distributed strain sensor based on the optical frequency domain reflectometer (OFDR) preserves its dominant position in short-distance measurement fields with high spatial resolution, such as biomedical treatment, soft robot, etc. However, owing to the weak intensity of the Rayleigh backscattered signal (RBS) in the single-mode fiber (SMF) and complex computation, the large strain changes cannot be precisely and rapidly demodulated by the traditional cross-correlation method. In this work, the OFDR with backscattering enhanced optical fiber (BEOF) is proposed and demonstrated for fast and large strain measurement. By enhancing the RBS amplitude, the signal-to-noise ratio (SNR) is improved, resulting in a higher similarity between the reference signal and test signal, which is beneficial for the expansion of the strain measurement range. Moreover, the adaptive local feature extraction and matching (ALFEM) algorithm is presented and demonstrated, which replaces the traditional cross-correlation method for strain demodulation and fast measurement. On account of the enhancement ratio of BEOF, the dominant characteristic data segment can be extracted from whole wavelength data. In the experiments, the enhancing ratio of BEOF is designed as 10, resulting in the spatial resolution reaches 400µm and the strain measurement range is greatly increased to 4800µɛ. Further, the effectiveness of the ALFEM algorithm has been verified, in which the strain demodulation time is approximately 25% of that of the traditional method. This scheme fully exploits the enhancement characteristic of the BEOF and is also applicable to the systems based on other types of BEOF, different strain changes and sensing distances.