For a long time, the development of maritime communication has been restricted by the low data rate, high-latency and high cost of the current communication systems. The upgrade of new generation mobile communication technologies is attracting more and more attention to conduct a shore-based broadband mobile communication network with high-latency and high reliability to serve the maritime industries. This paper presents a solution by means of building a ship-to-infrastructure (S2I) and a ship-to-ship (S2S) wireless communication networks for an offshore region. We characterize the S2I and S2S channels at 5.9 GHz band based on the channel measurements in realistic environments. The channel characteristics, including power delay profile, delay spread, propagation path loss, are extracted and analyzed. In view of the difference between marine and terrestrial communications, we analyze the influencing factors of the offshore water, including effective reflection, divergence and shadowing from the water surface, and diffraction loss caused by the earth curvature. We also predict the power coverage range and the channel capacity for S2I and S2S wireless communications. Finally, the communication performance is evaluated according to the channel measurement and characterization analysis. The research results can be a reference for the construction of maritime communication networks.