Precise measurement under high counting rates has been a major challenge for γ-ray spectroscopy, where signals generally pile up with each other and their characteristic values are deeply coupled. An off-line pile-up pulse recovery algorithm based on template matching is developed for LaBr3 scintillation detectors and has been applied to data from China Spallation Neutron Source (CSNS) Back-n white neutron beamline. As an improvement to the traditional Template Matching methods, the predetermined template shape is associated with pulse amplitudes, which is found crucial to achieve the best fitting results. Moreover, a universal strategy of setting the initial values of fitting allows to resolve signals that are separated in time by less than the characteristic rise time. Processing of simulated pulses demonstrates that the lower limit of interval to distinguish successive events is 10 ns, which is a significant improvement to the previous works. The algorithm performs well under a counting rate of 6×107 s−1, and is still effective up to 108 s−1. Analysis of experimental data indicates that this algorithm recovers over 98% count yield under a counting rates of no more than 4×106 s−1 in this work, providing a more reliable approach to deduce neutron-induced reaction cross sections.