The laser wavelength in self-sweeping laser is linearly changing in time from start to stop wavelength without use of optical elements and electrical drivers for frequency tuning. Absolute difference between the start and stop wavelength values (sweeping span) characterizing the sweeping process is one of the key characteristics of any tunable source. Owing to broad sweeping span (more than 10 nm) and simplicity, self-sweeping fiber lasers are attractive sources for applications demanding tunable radiation such as sensors interrogation, spectral analysis, optical frequency domain reflectometry and so on. Self-induced nature of the sweeping process leads to fluctuations of the sweeping span borders. We demonstrate in this talk implementation of fiber Bragg gratings (FBG) for control and stabilization of start and stop wavelengths in the self-sweeping laser. We showed that the short-wavelength FBG helps to initialize the sweeping process and long-wavelength FBG blocks the laser line sweeping in long-wavelength region. The last effect is associated with mismatch of longitudinal mode structures of the laser and FBG-based selector. As a result, fluctuations of the sweeping span borders decreased by one or two orders of magnitude down to several picometers. In addition, we studied influence of the parameters for FBG-based selectors such as reflections and mode structure on quality of sweeping range stabilization. The results allow to improve the characteristics of self-sweeping fiber laser which can be used for different sensing applications such as atmospheric remote sensing and interrogation of the sensors based on fiber Bragg gratings.