The Brillouin optical time-domain reflectometer (BOTDR) system, which is based on the Brillouin frequency shift (BFS) of the scattering spectrum, has been widely applied to monitor the temperature and strain in many fields. The measurement accuracy of the BFS directly affects the monitoring and location of the temperature change or strain events. In this study, the characteristics of the least-squares fitting optimal solution of the Brillouin power spectrum are theoretically investigated, and a half-peak fitting algorithm is proposed to measure the BFS with high accuracy and stability. In particular, it can precisely determine the double-peak spectrum and detect the position in the transition section of a temperature change or strain event. Furthermore, it can reduce calculation complexity and enhance measurement speed by dropping most of the data. For the fiber under test (FUT) with a length of 12-km, 200 groups of time-domain data were processed using a probe pulse of width 50 ns and sampling rate 1 GHz. The half-peak fitting algorithm increased the temperature measurement accuracy by ~1 fold, with ~20% calculation of full fitting. Meanwhile, it effectively eliminated the influence of minor peak in the doublepeak spectrum, and optimized the spatial resolution of the temperature change position to 0.1-m, which is the maximum limitation by sampling rate.