Grid is a distributed platform that makes the utilization of distributed and powerful sharing resources for those submitted applications more conveniently. Applications designed to execute on grid frequently require the simultaneous co-allocation of multiple resources to meet performance requirement. In particular, the problem of co-allocating grid resources that span multiple administrative domains is complicated by the possibility of deadlock and the lack of means for changing information between the independent applications. Motivated by this, this paper develops a new method for fast co-allocation of grid resources. The proposed method is based on Atomic Transaction and is free from deadlock. Experimental results demonstrate that the proposed method yields a significant performance improvement over other existing deadlock prevention methods.