Grid computing enables large-scale resource sharing and collaboration for solving advanced science and engineering applications. Central to the grid computing is the scheduling of application tasks to the resources. Various strategies have been proposed, including static and dynamic strategies. The former schedules the tasks to resources before the actual execution time and later schedules them at the time of execution. Static scheduling performs better but it is not suitable for dynamic grid environment. The lack of dedicated resources and variations in their availability at run time has made this scheduling a great challenge. In this study, we proposed the adaptive approach to schedule workflow tasks (dependent tasks) to the dynamic grid resources based on rescheduling method. It deals with the heterogeneous dynamic grid environment, where the availability of computing nodes and links bandwidth fluctuations are inevitable due to existence of local load or load by other users. The proposed adaptive workflow scheduling (AWS) approach involves initial static scheduling, resource monitoring and rescheduling with the aim to achieve the minimum execution time for workflow application. The approach differs from other techniques in literature as it considers the changes in resources (hosts and links) availability and considers the impact of existing load over the grid resources. The simulation results using randomly generated task graphs and task graphs corresponding to real world problems (GE and FFT) demonstrates that the proposed algorithm is able to deal with fluctuations of resource availability and provides overall optimal performance.