One of the major challenges in wide use of Grid workflow systems is fault tolerance and avoidance. Checkpointing schemes provide a way of fault detection and recovery. In our research, we focus on performance optimization of checkpointing schemes for Grid workflow systems. We propose a set of adaptive checkpointing schemes that dynamically adjust the checkpointing intervals online by using store-checkpoints (SCPs) and compare-checkpoints (CCPs). These schemes can efficiently utilize comparison and storage operations and significantly improve the performance. Further, these schemes can calculate the optimal numbers of checkpoints by which minimize the mean execution time. We also expand the schemes from single-task execution scenarios to multitask execution scenarios. Simulation results show these schemes outstandingly increase the likelihood of timely task completion when faults occur.