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A bi-objective Fuel efficient Green Vehicle Routing Problem (F-GVRP) with varying speed constraint is discussed in this paper as an extension of Green Vehicle Routing Problem (G-VRP). F-GVRP is modelled to minimize both route cost and fuel consumption using goal programming. The problem is solved using Particle Swarm Optimization with Greedy Mutation Operator and Time varying acceleration coefficient (TVa-PSOGMO). The objective of this paper is to study the behaviour of F-GVRP under varying speed environment and its impact on the route cost and fuel consumption. Experiments are conducted with constant and varying speed constraints and it is observed that better routing plan with minimum fuel consumption can be achieved under varying speed environment. [ABSTRACT FROM AUTHOR]