Grid computing is a computer network in which many resources and services are shared for performing a specific task. The term grid appeared in the mid-1990s and due to the computational capabilities, efficiency and scalability provided by the shared resources, it is used nowadays in many areas, including business, e-libraries, e-learning, military applications, medicine, physics, and genetics. In this paper, we propose WorkStealing-Grid Cost Dependency Matrix (WS-GCDM) which schedule DAG tasks according to their data transfer cost, dependency between tasks and load of the available resources. WS-GCDM algorithm is an enhanced version from GCDM algorithm. WS-GCDM algorithm balances load between all the available resources in grid system unlike GCDM which uses specific number of resources regardless how many resources are available. WS-GCDM introduces better makespan than GCDM algorithm and enhances system performance from 13% up to 17% when we experiment algorithms using DAG with dependent tasks.