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The process of computational grid resource scheduling generally falls into two phases: global resource scheduling and local resource scheduling. Under this pattern, global resource scheduling algorithms are different from the traditional resource scheduling algorithms of LRMSs (local resource management system, LRMS). In this paper, a general self- adaptive global resource scheduling algorithm for Computational Grid, BMQOS (Best Multi QOS) is presented. According to the personal resource requirement of a computational grid job, BMQOS globally selfadaptively weighs every index of the MQOS of candidate computational grid nodes and chooses an appropriate node for a job from the candidates finally. Applied in NPU Campus Computational Grid, this algorithm achieves good effect.