Abstract: In order to solve the resource scheduling problem in service grid environment to guarantee the need of user jobs complete time, an independent matchmaker was introduced into the three-element service grid model. The service grid model was formally illustrated based on the graph theory, and the necessary and sufficient conditions of complete match of user jobs and grid service resources were also proved. A grid services matchmaking system was constructed on the base of sensor feedback. The optimal matchmaking problem of the system was formally illustrated based on the running time weight matrix, and the optimal solution arithmetic was proposed based on the discrete event dynamic system theory. Simulation analysis shows that the arithmetic can improve the QoS (quality of services) performance parameter of the grid services matchmaking system, provide the user jobs completed time guarantee and meet the load balance need of grid service resources.