Automatic grasp planning is an active field in robotic research. Its main purpose is to find the contact points between the robotic hand and an object in order to grasp it efficiently. As the robotic hand has many degrees of freedom which induce a huge number of solutions, the search for the “best” solution became an optimization problem. The search of such a solution is conducted by a grasp quality measurement which will be called the objective (or fitness) function. This paper proposes a Multi-Objective Particle Swarm Optimization (MOPSO) approach to tackle the grasp planning problem. Its fitness functions are based in two different grasp quality measurements. The MOPSO approach is then tested in HandGrasp simulator with simple objects. The results will be compared with two simple Particle Swarm Optimization (PSO) approaches and demonstrate its performance.