In maritime networks, the communication links are characterized as high dynamics due to ship mobility and fluctuation of the sea surface. The performance of traditional transmission protocols is poor in maritime networks. Thus, some researchers have considered using Delay Tolerant Network (DTN) to improve the performance of data transmission in maritime environment. Most existing work on maritime DTNs uses simulation to evaluate the transmission performance in maritime DTNs. In this paper, we develop a theoretical model to analyze the performance of data transmission in maritime DTNs. We first construct a model to describe the ship encounter probability. Then, we use this model to analyze the data delivery ratio from ships in the seaway to the base station (BS) on the coast. Based on the data of tracing the ships navigating in a realistic seaway, we develop a simulator and validate the theoretical models. In addition, by comparing the performance of DTN transmission protocol and traditional end-to-end transmission protocol, we confirm that DTN protocol can effectively improve the performance of data transmission in maritime networks.