Maritime domain awareness deals with the situational understanding of maritime activities that could impact the security, safety, economy or environment. It enables quick threat identification, informed decision making, effective action support, knowledge sharing and more accurate situational awareness. In this paper, we propose a novel computational intelligence framework, based on genetic programming, to predict the position of vessels, based on information related to the vessels past positions in a specific time interval. Given the complexity of the task, two well known improvements of genetic programming, namely geometric semantic operators and linear scaling, are integrated in a new and sophisticated genetic programming system. The work has many objectives, for instance assisting more quickly and effectively a vessel when an emergency arises or being able to chase more efficiently a vessel that is accomplishing illegal actions. The proposed system has been compared to two different versions of genetic programming and three non-evolutionary machine learning methods, outperforming all of them on all the studied test cases.