This study presents a fatigue model for constant and variable amplitude cyclic loading by combining kinetic theory of fracture (KTF) with peridynamics (PD). The KTF is applicable to constant and variable amplitude loading, and cumulative damage is inherent in the assumptions. Also, it is extremely suitable for implementation in the PD model of laminates. The standard stress versus cycles to failure data for unnotched laminates provides the determination of necessary parameters for the KTF. Using the test data generated by the Air Force Research Laboratory under the Tech Scout Project, the fidelity of this model is established by simulating the open-hole quasi-isotropic composite laminates under cyclic loads for stiffness reduction and failure progression. The PD predictions agree with the measured reduction in stiffness as a function of number of load cycles. Also, the progressive damage predictions capture the general characteristics of the experimentally observed damage patterns.