In this paper, a new algorithm is presented which is applied to a real world Vehicle Routing Problem (VRP) of a provision company in the island of Crete in Greece. The company serves 116 customers located in Crete. This real world problem is solved effectively by a hybrid Island Memetic Algorithm (IMA) which employs Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Local Search (ILS). The proposed algorithm is also compared to five other approaches both on the real world problem and on classic benchmark instances from the literature. Methods such as GRASP, local search and Iterated Local Search (ILS) are employed as subroutines with certain probabilities in the algorithms. Furthermore, it is also demonstrated how premature convergence can be prevented by adopting specific strategy. Computational results show the superiority of the proposed hybrid Island Memetic Algorithm