With the rising and research deepening of new technologies such as laser radar, gravitational wave detection, and optical atomic clock, The breadth and depth of applications covered by optical precision measurement are expanding, the stability of the traditional free operation of the laser is difficult to meet the application requirements, ultra-narrow linewidth, low noise, and long-term stability of light source has become the urgent goal in this field. Fiber laser has the characteristics of compact structure, easy integration, and narrow limit line width. Through noise suppression and frequency stabilization technology, fiber laser can output ultra-high stability and ultra-narrow linewidth laser. In recent years, ultra-narrow line width fiber laser has gradually become a hot research direction. In this paper, starting from the theory of noise of fiber laser, the noise source, classification, and testing method of fiber laser are introduced, based on the theory of noise, the principle of different intensity and frequency noise suppression technology, development course, and the current progress of fiber laser are summarized, respectively, and the development tendency of narrow linewidth fiber laser is discussed.