Abstract: As a component of a grid job, a grid service is required to select suit able resource from global wide providers so that the different resource assignme nts will have distinctive impact on the utility of the job,which results in SRA(service resource assignment) problem.Addressing it a novel method TDRA (tree decomposition based resource allocation algorithm), based on tree- decomposition of grid resource dependency graph ,was choosed to form the correct vertex elemination order on which the variables were iteratively relaxed untill the optimised result was reached. The method indicates the complexity of TDRA i s polynominal instead of exponential,which proves available to solve SRA problem s. As a conclusion the further work of this research was also discussed.