In this paper, the green vehicle routing problem with time windows constraint is studied in the presence of a heterogeneous fleet of vehicles and filling stations. In addition, the number of vehicles and their fuel tank capacity are both limited. The main contribution of this study is the simultaneous consideration of these features, which makes the problem more practical. For this purpose, a mixed integer linear programming model that minimises the transportation costs and (or carbon dioxide) emissions, is proposed. Furthermore, a genetic algorithm and a population-based simulated annealing are developed to find high-quality solutions for large-scale instances. To validate the proposed model and algorithms, 28 instances are generated using a benchmark database. The computational results demonstrate that both algorithms provide efficient solutions regarding the objective function value and CPU time. Finally, a comprehensive sensitivity analysis is carried out to show the importance of features mentioned above. [Received: 7 October 2016; Revised: 27 December 2018; Accepted: 13 January 2019]