A new Monte-Carlo model is proposed in which the viscosity of entangled polymer melts is obtained directly from their creep compliance. In the model, the melt is represented by a dense array of chains which interact through entanglements placed on the sites of a diamond lattice. The chains are allowed to slip through entanglements by use of a thermally activated process. For chains of monodisperse length M, we find that the viscosity scales as eta(0) similar to M(3.46+/-0.05), in agreement with experimental observation.