Distribution of goods is one of the main issues that directly affect the performance of the companies since efficient distribution of goods saves energy costs and also leads to reduced environmental impact. The multi-compartment vehicle routing problem (MCVRP) with a heterogeneous fleet of vehicles is encountered when dealing with this situation in many practical cases. This paper is motivated by the fuel delivery problem where the main objective of this research is to minimize the total driving distance using a minimum number of vehicles. Based on a case study of twenty petrol stations in northeastern Thailand, a novel two-phase heuristic, which is a variant of the Fisher and Jaikumar Algorithm (FJA), is proposed. The study first formulates an MCVRP model and then a mixed-integer linear programming (MILP) model is formulated for selecting the numbers and types of vehicles. A new clustering-based model is also developed in order to select the seed nodes and all customer nodes are considered as candidate seed nodes. The new Generalized Assignment Problem model (GAP model) is formulated to allocate the customers into each cluster. Finally, based on the traveling salesman problem (TSP), each cluster is solved in order to minimize the total driving distance. Numerical results show that the proposed heuristic is effective for solving the proposed model. The proposed algorithm can be used to minimize the total driving distance and the number of vehicles of the distribution network for fuel delivery.