Dynamic moduli and energy dissipation capability of polymer hybrid nanocomposite reinforced with carbon fiber (CF) coated by carbon nanotube (CNT) which makes a fuzzy fiber nanocomposite (FFNC) are estimated through a micromechanical model. An analytical expression is derived to extract the damping properties in the frequency domain. Then, a separate phase known as interphase whose properties vary gradually is taken into account to model the CNT/polymer interactions. The CNT waviness and random orientation are also included. Acceptable agreements in comparison with the molecular dynamics simulations and experiments prove the accuracy of the proposed model. Moreover, the maximum reachable volume fraction of CNTs is studied considering the radius of gyration of polymer chain, the CNT aspect ratio (CNTAR), radius, and waviness amplitude. The effects of the CNT inter-tube distance (CNTID), waviness, CNTAR, and the loading frequency are examined on the energy dissipation and storage capability, and hysteresis loop of FFNC. It is found that the FFNC effective dynamic moduli enhance by increasing the CNTAR, while the CNTAR becomes less influential as the CNTID increases. Furthermore, as the frequency increases, the area of the hysteresis loop is decreased. Whereas the hysteresis loop is converted to a straight line beyond the frequency of about 1e17 Hz.