In order to meet the wide demands of single longitudinal mode continuous wave laser in various fields such as optical communication, optical sensing, precision measurement, quantum technology, and atomic physics etc., the stability and signal-to-noise ratio of the single longitudinal mode laser has to be improved. This paper discusses the intensity noise which plays a major role in output stability of a single longitudinal mode laser, and shows its main source and generation mechanism. On this basis, combined with comparative analysis of various methods, this paper gives the recent developments of suppression means of intensity noise. Aimed at improving output stability of single longitudinal mode fiber laser in high power laser facility, relevant study using semiconductor optical amplifier is given, which suppressed the intensity noise.