The transmission rate between two nodes is usually very low in underwater acoustic networks due to the low available bandwidth of underwater acoustic channels. Therefore, increasing the transmission parallelism among network nodes is one of the most effective ways to improve the performance of underwater acoustic networks. In this paper, we propose a new collision-free hybrid medium access control (MAC) protocol for distributed multi-channel underwater acoustic networks. In the proposed protocol, handshaking and data transmission are implemented as a pipeline on multiple acoustic channels. Handshaking is implemented using the time division multiple access (TDMA) technique in a dedicated control channel, which can support multiple successful handshakes in a transmission cycle and avoid collision in the cost of additional delay. Data packets are transmitted in one or multiple data channels, where an algorithm for optimizing the transmission schedule according to the inter-nodal propagation delays is proposed to achieve collision-free parallel data transmission. Replication computation technique, which is usually used in parallel computation to reduce the requirement of communication or execution time, is used in the data packet scheduling to reduce communication overhead in distributed environments. Simulation results show that the proposed protocol outperforms the slotted floor acquisition multiple access (SFAMA), reverse opportunistic packet appending (ROPA), and distributed scheduling based concurrent transmission (DSCT) protocols in throughput, packet delivery rate, and average energy consumption in the price of larger end-to-end delay introduced by TDMA based handshaking.