In this paper, a simulated annealing algorithm is presented for the Bandwidth Minimization Problem for Graphs. This algorithm is based on three distinguished features including an original internal representation of solutions, a highly discriminating evaluation function and an effective neighborhood. The algorithm is evaluated on a set of 113 well-known benchmark instances of the literature and compared with several state-of-the-art algorithms, showing improvements of some previous best results. Key words: Bandwidth Minimization, Heuristics, Simulated Annealing