In underwater acoustic applications, time synchronization errors accumulate severely with time, owing to the unpredictable propagation delay change induced by mobility and low sound propagation speed. In previously reported schemes, error accumulation during underwater acoustic time synchronization occurred, decreasing their performance and affecting their applicability. To overcome this limitation, we propose packet-train-aided time synchronization (PTA-Sync) for underwater acoustic application. The proposed PTA-Sync adaptively tracks one-way travel time (OWTT) change using three-dimensional linear velocity vector, the transmit time difference and arrival time difference of two adjacent packets in a packet train, and the position information of a mobile reference node. Thus, this scheme enables us to reduce the synchronization error accumulation rate by estimating the propagation delay change more accurately. Simulation results show PTA-Sync achieves higher accuracy than existing OWTT-based synchronization schemes. Thus, PTA-Sync can be effectively used in underwater exploratory activities because it can successfully reduce time synchronization errors.