This paper presents a dedicated local search method for the Multi-Objective Resource-Constrained Project Scheduling Problem (MORCPSP). This problem consists in the scheduling of a set of activities and the allocation of a set of limited resources with the aim to optimize more than one objective. The minimization of the maximum completion time of the project and the total weighted start times were considered; both are inspired in Project Management issues. To validate the performance of the proposal method, a set of benchmark instances were tested. The computational results point out the efficiency of the proposed approach on the improvement of Pareto Fronts.