The fiber Bragg grating sensor reflects the change of the physical quantity measured by the change of the center wavelength, so it is of great significance to improve the demodulation accuracy of the wavelength of the fiber Bragg grating. Most of the traditional demodulation algorithms cannot accurately demodulate overlapping spectra and distorted spectra because of poor anti-noise performance and limited demodulation accuracy, which limits the development of demodulation systems. The high-precision demodulation algorithm can realize accurate demodulation of sensor networks by solving the problems such as poor anti-noise performance and low peak-finding accuracy. The article introduces the sensing principle of fiber grating, explains the main types and production method on fiber grating, and summarizes the high-precision wavelength demodulation algorithms of fiber Bragg grating in recent years. The principle, advantages, and disadvantages of each demodulation algorithm are explained which is divided into two types: single-peak peak-finding algorithm and multi-peak peak-finding algorithm. And the article briefly analyzes and prospects the future of high-precision demodulation algorithms of fiber Bragg grating.