The green capacitated vehicle routing problem (GCVRP) has attracted the attention of many researchers recently, due to the increasing global climate issues. This study presents an interactive fuzzy approach for solving green capacitated vehicle routing problem with imprecise travel time for each vehicle and supplier demands. Triangular fuzzy numbers are proposed for modeling uncertainty, and optimization problem is considered as a bi-objective possibilistic mixed-integer programming (PMIP) model. Possibilistic mixed-integer programming and a fuzzy analytical hierarchical process approach (FAHP) are combined to optimize two objective functions: (1) minimum total fuel consumption and (2) maximum total green score. In the first objective function, the fuel consumption ratio model is used. In this model, the fuel consumption is considered as function of travel time and total load of the vehicle. In the second objective function, suppliers are evaluated in terms of environmental factors with the fuzzy AHP method. The normalized weights are assigned to suppliers as a green score. A conciliating solution is obtained by solving this bi-objective mixed integer programming model. The proposed model and solution approach is applied for an automotive company in Turkey. According to the results obtained, a suggestion for a vehicle routing is proposed.