Time synchronization of underwater acoustic sensor networks is an important prerequisite for the normal operation of multiple access transmission. However, the separated research of the two can easily lead to repeated sending of control packets, resulting in the waste of time and energy resources. Therefore, we propose time synchronization with multiple-access data transmission protocol (TSMP) in underwater sensor networks. In this protocol, time synchronization and multiple-access data transmission are combined to form an effective underwater data transmission system, reducing exchanged message and saving time and energy. In addition, there are no reference nodes as standard time. We are pursuing local time synchronization that only nodes that communicate with each other are synchronized. The time synchronization of TSMP is based on the Doppler method to calculate the relative speed between nodes. Considering the effect of the relative movement between nodes on the propagation delay, the accuracy of transmission delay is improved. Then, the receiver adds the local time to the value of total transmission delay. This allows the receiver and the sender to synchronize. Simulation results show TSMP has a better performance in terms of the packet delivery fraction, synchronization errors and energy efficiency.