Abstract: A generalized second-order time difference of arrival (GSTDOA) underwater acoustic location model is proposed to solve the problem of the acoustic beacon localization with periodic offset. The traditional second-order time difference of arrival (STDOA) model is extended to the generalized case where the localization node is not required to be selected at equal periodic intervals. Therefore, the localization precision can be further improved. Besides, the RELAX algorithm is introduced to optimize the location node, and the density-based spatial clustering algorithm is introduced to improve the robustness of the input outliers. The simulation data and lake trail data show that the new model has higher localization precision than the traditional time difference of arrival (TDOA) model or the STDOA model. The localization model proposed in this paper realizes high-precision localization for the periodic drift acoustic beacon with the localization precision of 3 m in typical application scenarios.