With the increase of High Performance Computation (HPC) system scale, it's very important to increase the efficiency of the checkpoint. A model to compute the quasi-optimal period for hierarchical checkpoint protocol was proposed. First, the execution of an application in HPC system was assessed, and checkpoint period optimization problem was abstracted as the nonlinear checkpoint cost model. Second, the hierarchical checkpoint cost formula was derived by simulating the possible fault location; two deceleration parameters and an acceleration parameter were introduced to reflect the impact of message logging on the hierarchical checkpoint. The simulation results show that, compared with the quasi-optimal period checkpoint cost, the average error value of the proposed model is below 5%, which is 20% less than that of the traditional model based on Markov chain. The proposed model can signally increase the efficiency of the hierarchical checkpoint protocol; meanwhile enhance the availability of the HPC system.