In this paper, we propose an approximation scheme to solve large stochastic mixed-integer programming (SMIP) problems with fixed recourse. We refer to this as the Scenari o Updating Method. The algorithm is based on solving instances of the problem, which cont ain only a subset of the scenarios in the scenario tree. At each iteration, th e subset of scenarios is updated by adding only those scenarios which suggest a significant potential for change in the objective function value. The algorithm is terminated when the potential for change is insignificant.Different selection and updating rules are discussed.