A cyclic cohesive zone model is applied to characterize the fatigue crack growth behavior of a IN718 superalloy which is frequently used in aerospace components. In order to improve the limitation of fracture mechanics-based models, besides the predictions of the moderate fatigue crack growth rates at the Paris’ regime and the high fatigue crack growth rates at the high stress intensity factor ΔK levels, the present work is also aimed at simulating the material damage uniformly and examining the influence of the cohesive model parameters on fatigue crack growth systematically. The gradual loss of the stress-bearing ability of the material is considered through the degradation of a novel cohesive envelope. The experimental data of cracked specimens are used to validate the simulation result. Based on the reasonable estimation for the model parameters, the fatigue crack growth from moderate to high ΔK levels can be reproduced under the small-scale yielding condition, which is in fair agreement with the experimental results.