A creep prediction model of concrete considering the viscoelasticity of interface transition zone was proposed based on the Laplace transform principle to analyze the influence of interface transition zone on the creep performance of concrete. The proposed model was compared with a model of concrete creep non-considering interface transition zone and verified by the related experiments. The results show that the data predicted by the concrete creep model considering the interfacial transition zone is consistent with the experimental results. The model can be used to analyze the effect of interface transition zone on the creep properties of concrete besides the experiments. The specific creep of concrete specimens with different fly ash contents (i.e., 0, 30% and 60%) is increased by 45.7%, 25.1% and 66.7%, respectively, when the loading age is 365 d due to the interface transition zone. The contribution of the interface transition zone of concrete specimens with different fly ash contents to the creep of concrete at different loading ages was analyzed via the prediction by the model. The interfacial transition zone of concrete with fly ash to the concrete creep contributes greater than that without fly ash. The interface transition zone of the baseline group in the later period has an increasing contribution to the concrete creep due to the continuous weakening of the interface transition zone under the load. For the concrete specimens with fly ash, the interface transition zone continuously enhances and the contribution of the interface transition zone to the creep of concrete continuously reduces with the increase of loading age because of the fly ash secondary hydration. The analysis of the influence of interface transition zone parameters on the concrete creep indicates that the concrete creep of different interface transition zones can be well described when the interface transition zone elasticity constant is in the range of 0.000 1<E_itz<0.01 and the viscosity coefficient is in the range of 0.1<η_itz<10.