The asymmetrical reflection peaks are easy to appear when fiber Bragg grating (FBG) is packaged and the conventional fitting method has a large error in demodulation. In this paper, a new algorithm of fiber Bragg grating demodulation based on digital correlation matching is proposed to solve this problem. The effectiveness and feasibility of the new algorithm are studied by the numerical simulations and water-bath experiment. The experimental results show that the error of this algorithm is about 67% less than that of the conventional Gauss fitting algorithm under the condition of asymmetrical reflection peak. The algorithm of fiber grating demodulation based on digital correlation matching enlarges the application range of demodulation algorithm, improves the demodulation accuracy of asymmetrical reflection peaks, and maintains the effectiveness of FBG sensing.