In this study, a three-phase multiscale model is developed to study the elastic behavior of the carbon nanotube-reinforced polymer composites. The cohesive zone model is implemented to model the carbon nanotubes debonding. The effects of weight fraction and aspect ratio of the carbon nanotubes as well as the strength of the interfacial adhesion on the effective elastic response of the nanocomposite have been investigated. A good agreement is obtained between the predicted and available experimental results when the cohesive interface is introduced in the model. The results show that carbon nanotube/polymer interfacial strength has more significant effect on the nanocomposites modulus and stiffness for higher values of weight fraction and aspect ratio.