A unified strategy for dynamic mapping in grid computing environments is brought forward. Immediate mode and batch mode are symbiotic and can switch adaptively in this strategy, and MCT for the immediate mode mapping and an improved Sufferage algorithm for the batch mode scheduling are utilized. And the utility functions meet the requirements of diverse QoS of tasks. The experimental results indicate that the improved scheme is superior to the benchmark algorithms in performance and adaptable to the varying task flow in grid computing environments.