In this paper, we study the stopping sets, stopping distance and stopping redundancy for binary linear codes.Stopping redundancy is a new concept proposed by Schwartz and Vardy recently for evaluating the performance of a linear code under iterative decoding over a binary erasure channel (BEC). Since the exact value of stopping redundancy is difficult to obtain in general, good lower and upper bounds are important. We obtain a new general upper bound on the stopping redundancy of binary linear codes which improves the corresponding results of Schwartz and Vardy.