Auction-based resources allocation and jobs scheduling are key techniques in grid computing system. In this paper, we propose an on-line auction method to allocate grid resource, where the resource providers arrive dynamically and resource user has to make a multi-attribute decision whether to trade jobs or not before the end of current round. In this method, a trade-some-if-beneficial algorithm is designed to help resource user determine the finial winners with incomplete information. Experiments show that our approach can satisfy the resource user’s quality demand on speed, memory and deadline even in an on-line setting. The simulating results also highlight how a resource user can improve his performance using this algorithm.