In this research, a three dimensional analytical method is presented for predicting the dynamic properties of polymer nanocomposites. In the present method elastic-viscoelastic correspondence principle is applied on the simplified method of cell, and loss modulus, storage modulus, loss factor and Hysteresis loop are obtained using energy method as well as force balance method. The considered nanocomposite possesses Polypropylene as a matrix reinforced by vapor grown carbon fibers. The rrepresentative volume element consists of three isotropic phases including fiber, interphase and matrix with linear viscoelastic behavior based on Zener model. Furthermore the nanocomposite constituents dynamic properties are extracted in frequency domain by employing Fourier transform method and Schapery model First to assure the validation of the model, the results are compared with experimental results. Parametric studies such as the effects of number of subcells, fibers volume fraction (FVF) and aspect ratio, matrix/fiber link strength factor and interphase loss factor on the nanocomposite dynamic properties are investigated.. Obtained results reveal that the presented method has acceptable speed and accuracy. Moreover fiber aspect ratio and FVF increasing leads to decrease the nanocomposite hysteresis loop area, subsequently its damping capacity reduces. Interphase also contains considerable effects on the nanocomposite dynamic properties, so its modeling has a great importance.