The construction of a timetable represents a critical part on the development of the yearly service plan for railway operations. The Train Timetabling Problem (TTP) aims to find a timetable that must respond both to commercial needs and certain capacity and security related constraints. The combination of the latter, makes the TTP a complex and time consuming process. While most approaches on the literature offers exact solving models, once they are applied on real-size instances, they fail to solve the problem within a reasonable amount of time. Reason for which, heuristic or relaxation techniques are extensively used. In this paper, we first propose an alternative mathematical model to tackle the TTP. Next, we present a Genetic Algorithm implementing our model in order to rapidly obtain near-optimal train timetables. Finally, we test the implementation of our model on a case study based on the German railway network.