Distributed Bragg reflection (DBR) single longitudinal mode fiber lasers have been widely studied and applied due to their simple resonant cavity structure and good stability. However, the narrow tuning range of current DBR lasers limit their applications in many important fields such as spectral synthesis, laser frequency locking, and coherent detection, etc. Therefore, how to improve its tuning range is of greater research value. And improving the mode-free hopping tuning range of DBR fiber lasers has become the research objective in this study.First of all, according to the principle that the center wavelength of fiber grating drifts is caused by resonant cavity temperature change, the equivalent length theory of the fiber grating, the longitudinal mode spacing theory, and the relationship between the gain spectrum of the doped fiber and the intracavity mode competition, the mechanism of DBR single longitudinal mode fiber laser to achieve single longitudinal mode output and the variation of the longitudinal mode in the resonant cavity during the temperature tuning process are theoretically analyzed. Secondly, DBR single longitudinal mode fiber lasers were built based on the theoretical analysis, and two DBR lasers with different equivalent cavity lengths were constructed by using two different lengths of doped fibers. A temperature controller built with a Thermoelectric Cooler (TEC) and a brass sheet was used to control the temperature of the resonant cavity, and the variation of the center wavelength of the output laser and the longitudinal mode of the output laser during the change of the resonant cavity temperature from 0 ℃ to 100 ℃ were tested.As a result, the conditions that the cavity length of the resonant cavity of DBR single longitudinal mode fiber laser needs to meet in order to realize the temperature tuning without hopping mode are deduced. Besides, different single and multiple longitudinal mode output results during temperature tuning of lasers with different equivalent cavity lengths verify the correctness of the analytical result of cavity length constraint condition for DBR single longitudinal mode laser (Fig.3, Tab.1). And then, 8 mm high-concentration Yb³⁺ doped single mode fiber is used to achieve a stable single-longitudinal-mode laser at the wavelength of 1064 nm with the distributed Bragg reflection method. The effective cavity length of the DBR resonator is 16 mm and the maximum laser output power is 7.4 mW. The single longitudinal mode tuning of 0.824 nm without mode hopping is achieved by varying the resonant cavity temperature (Fig.4). With the low loss circulator and the fiber mirror to multiply delay fiber length of the heterodyne method to improve measurement accuracy (Fig.7), the measured maximum linewidth of the laser is 4.4 kHz. The relative intensity noise of the laser was tested using a photodetector. The relaxation oscillation peak of the output laser is located at 900 kHz with a relative intensity noise of -110 dB/Hz. The relative intensity noise is -145 dB/Hz when the frequency is greater than 1.5 MHz. In summary, through theoretical and experimental studies, a 1064 nm, mode-hopping-free tuning range of 0.8 nm distributed Bragg reflective single longitudinal mode fiber laser was proposed, and a series of its key parameters were tested, which has certain application value.