Time synchronization plays a critical role in distributed network systems. In this paper, we investigate the time synchronization problem in the context of underwater sensor networks (UWSNs). Although many time-synchronization protocols have been proposed for terrestrial wireless sensor networks, none of them can be directly applied to UWSNs. This is because most of these protocols do not consider long propagation delays and sensor node mobility, which are important attributes in UWSNs. In addition, UWSNs usually have high requirements in energy efficiency. To solve these new challenges, innovative time synchronization solutions are demanded. In this paper, we propose a pair wise, cross-layer, time-synchronization scheme for mobile underwater sensor networks, called DA-Sync. The scheme proposes a framework to estimate the Doppler shift caused by mobility, more precisely through accounting the impact of the skew. To refine the relative velocity estimation, and consequently to enhance the synchronization accuracy, the Kalman filter is employed. Further, the clock skew and offset are calibrated by two runs of linear regression. Simulation results show that DA-Sync outperforms the existing synchronization schemes in both accuracy and energy efficiency.