In this paper, we present a Multi-objective Particle Swarm Optimizer (MOPSO) based on a decomposition approach, which is proposed to solve Constrained Multi-Objective Aerodynamic Shape Optimization Problems (CMO-ASOPs). The constraint-handling technique adopted in this approach is based on the well-known epsilon-constraint method. Since the epsilon-constraint method was initially proposed to deal with constrained single-objective optimization problems, we adapted it so that it could be incorporated into a MOPSO. Our main focus is to solve CMO-ASOPs in an efficient and effective manner. The proposed constrained MOPSO guides the search by updating the position of each particle using a set of solutions considered as the global best according to both the decomposition approach and the epsilon-constraint method. Our preliminary results indicate that our proposed approach is able to outperform a state-of-the-art MOEA in several CMO-ASOPs.