In this paper we develop a Load Balancing scheme for networks based on the MPLS framework. The proposed algorithm (DYLBA - Dynamic Load Balancing Algorithm) implements a local search technique where the basic move is the modification of the route for a single Label Switched Path. Experiments under a dynamic traffic scenario show a reduced rejection probability especially with long-lived connection requests, thus providing a better use of resources when compared to existing constraint-based routing schemes for traffic engineering in MPLS networks.