The default fault tolerance mechanism of Spark is setting the checkpoint by programmer. When facing data loss, Spark recomputes the tasks based on the RDD lineage to recovery the data. Meanwhile, in the circumstance of complicated application with multiple iterations and large amount of input data, the recovery process may cost a lot of computation time. In addition, the recompute task only considers the data locality by default regardless the computing capabilities of nodes, which increases the length of recovery time. To reduce recovery cost, we establish and demonstrate the Spark execution model, the checkpoint model and the RDD critically model. Based on the theory, the criticality checkpoint management (CCM) strategy is proposed, which includes the checkpoint algorithm, the failure recovery algorithm and the cleaning algorithm. The checkpoint algorithm is used to analyze the RDD charactersitics and its influence on the recovery time, and selects valuable RDDs as checkpoints. The failure recovery algorithm is used to choose the appropriate nodes to recompute the lost RDDs, and cleaning algorithm cleans checkpoints when the disk space becomes insufficient. Experimental results show that: the strategy can reduce the recovery overhead efficiently, select valuable RDDs as checkpoints, and increase the efficiency of disk usage on the nodes with sacrificing the execution time slightly.