The positioning of autonomous underwater vehicle (AUV) is the core technology of ocean engineering. Due to the positioning error of inertial navigation system (INS) accumulate with time, underwater acoustic positioning system (UAPS) could be used. In fact, INS/UAPS integrated navigation system is widely-used nowadays. AUV could estimate its positioning coordinates in time by receiving and processing the acoustic signals from UAPS. Few studies have focused on how to estimate the time offset of UAPS. In this paper, two method to obtain the AUV’s position and time offset are supplied based on synchronous spherical intersection model. The closed-form solution and Newton iteration could both obtain the AUV’s position and time offset. However, the positioning accuracy of closed-form solution is generally poor and cannot meet the requirements of underwater operations. Though Newton iteration method could be used to supply high positioning accuracy and time offset with UAPS, it occupies more time. Through simulation experiments by MATLAB, it could be proved that the Newton iteration method has higher positioning accuracy and accurate time offset than closed-form solution, but it takes more time to calculate.