The maritime Internet of Things (IoT) has recently emerged as a revolutionary communication paradigm where a large number of moving vessels are closely interconnected in intelligent maritime networks. However, the tremendous growth of vessel trajectories, collected from the combined satellite-terrestrial AIS (automatic identification system) base stations, could lead to unsatisfactory maritime safety and efficacy. To promote smart traffic services in maritime IoT, it is necessary to accurately and robustly predict the spatiotemporal vessel trajectories. It is beneficial for collision avoidance, maritime surveillance, and abnormal behavior detection, etc. Motivated by the strong learning capacity of deep neural networks, this work proposes an AIS data-driven trajectory prediction framework, whose main component is a long short term memory (LSTM) network. In particular, the vessel traffic conflict situation modeling, generated using the dynamic AIS data and social force concept, is embedded into the LSTM network to guarantee high-accuracy vessel trajectory prediction. In addition, a mixed loss function is reconstructed to make our prediction results more reliable and robust in different navigation environments. Both quantitative and qualitative experiments on realistic vessel trajectories have demonstrated that our method could achieve satisfactory prediction performance in terms of accuracy and robustness.