In this paper we present an ant colony optimization (ACO) algorithm for the Blocks Relocation Problem (BRP). The method is applied to both versions of the problem most commonly considered in literature, i.e., the restricted (rBRP) and the unrestricted (uBRP) BRP with distinct due dates. In case of the uBRP a new heuristic is proposed and incorporated in a standard greedy algorithm. The performance of the basic greedy approach is enhanced by extending it to the ACO metaheuristic. In it, a novel approach for defining the pheromone matrix is proposed. More precisely, it only stores a small amount of information instead of the complete bay state. Further, we show that the proposed ACO method can easily be adapted for solving the BRP in which the objective function is related to the crane operation time. Our computational results show that the proposed approach manages to outperform existing methods for the BRP.