This paper proposes a metaheuristic algorithm to solve the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDHFVRP). The problem consists of determining the customers and the vehicles to be assigned to each used depot and the routes to be performed to fulfill the demands of a set of customers. The objective is to minimize the sum of the fixed cost associated with the used vehicles and of the variable traveling costs related to the performed routes. The proposed approach is based on a modified genetic algorithm, which generates an initial population with heuristic solutions obtained from the well-known (LKH) heuristic algorithm for the TSP together with the solution of a mathematical model for the shortest path problem. In addition, two recombination methods and a mutation operator are considered. Computational experiments on benchmark instances show that the proposed algorithm can obtain high-quality solutions within short computing times.