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Commercial systems based on modem in underwater acoustic networks have two critical characteristics, low transmission rates and long preambles. It drastically degrades the performance of existing MAC protocols in the real world. In order to resolve this problem, this paper analyzed the impact of the modem characteristics on the random access-based MAC and handshake-based MAC, which are two major types of MAC protocols for underwater acoustic networks. An On-Demand Time Sharing MAC (COD-TS) based on cluster was introduced and analyzed, which adopted cluster technique to enable local schedule and on-demand response feature. COD-TS protocol for one hop network was introduced at first, the corresponding throughput model was proposed. After that, the scheme was extended to multi-hop scenarios. Simulation results show that the throughput of the proposed scheme is better compared with the existing Slotted ALOHA protocol and the RTS/CTS protocol. 