This paper describes the computer simulation of irradiation growths induced by neutron irradiations in zirconium using a combination of Molecular Dynamics (MD) and Kinetic Monte Carlo (KMC) methods. First, we performed the MD simulation of the displacement cascade on a defect cluster to study the interaction between the defect cluster and the displacement cascade. The MD simulations provide a lot of information on the amount of the defect production and the subsequent morphological change in the defect cluster. The results are used to make simple models that describe the nature of the displacement cascade overlap on the defect clusters. The models are then implemented into the KMC simulation code to extend the length- and time-scale of the simulation, which allows us to evaluate directly the defect cluster accumulations during a long-term irradiation. The irradiation growth strain resulting from the defect cluster accumulations is simply evaluated, and compared to an available experimental data. The comparison suggests that the displacement cascade overlap plays an important role on the irradiation growth, and, consequently, the KMC method with the simple models must be appropriate for the simulations of the irradiation growth.