In this work, we have developed a non-ordinary state-based peridynamic model for multiple crack initiation and propagation due to compression-compression fatigue load. In each loading cycle, the fatigue loading is redistributed among the peridynamic solid body, leading to the progressive fatigue damage initiation and propagation in an autonomous fashion. The proposed fatigue model parameters are firstly validated by 3D numerical benchmark tests, and then it is applied to simulate widespread fatigue damage evolution of the aircraft wing corner box. The modified constitutive damage model has been implemented into the peridynamics framework at finite strain. Furthermore, the criterion algorithm from multiple initiation to propagation is discussed. It is shown that the numerical results obtained from peridynamics simulations are in general agreement with those from the experiment data. The comparison of experimental and numerical results indicates that the proposed non-ordinary state-based peridynamics fatigue model has the ability to capture the multiple crack initiation and propagation and other features of the aluminium alloy material.