This work presents a new multiobjective algorithm based on ant colonies, which is used in the construction of the multicast tree for data transmission in a computer network. The proposed algorithm simultaneously optimizes cost of the multicast tree, average delay and maximum end-to-end delay. In this way, a set of optimal solutions, know as Pareto set, is calculated in only one run of the algorithm, without a priori restrictions. The proposed algorithm was inspired in a Multi-objective Ant Colony System (MOACS). Experimental results prove the proposed algorithm outperforms a recently published Multiobjective Multicast Algorithm (MMA), specially designed for solving the multicast routing problem