In order to solve the problems of poor cross-correlation stability and slow minimum mean square convergence in optical fiber vibration location algorithm, recursive least squares algorithm, moving average principle and early-late gate principle were adopted. A stable and fast response optical fiber vibration positioning system was designed. Optical path was based on double Mach-Zehnder interference structure. Hardware platform used high-speed acquisition board and field-programmable gate array to realize positioning. Repeated knocking experiments were carried out on 160m optical path. The obtained vibration data were computed separately in several segments. After removing the maximum and minimum values, the residual positioning results were averaged to improve the positioning accuracy. The results show that, as the number of iterations increases, recursive least squares method can stabilize the single positioning result without migration, compared with cross-correlation. Convergence rate is about 3 times of minimum mean square. At sampling rate of 10MHz, actual response time of the system is about 0.3s. The range of positioning error is ±6m. The positioning is stable and reliable. This research has positive significance for the improvement of location algorithm and positioning accuracy in optical fiber positioning system.