A fuzzy fiber reinforced composite (FFRC) reinforced with wavy zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is analyzed in this study. The distinct constructional feature of this composite is that the wavy CNTs are radially grown on the surface of carbon fibers. To study the effect of the waviness of CNTs on the elastic properties of the FFRC, analytical models based on the mechanics of materials (MOM) approach is derived. Effective elastic properties of the FFRC incorporating the wavy CNTs estimated by the MOM approach have been compared with those predicted by the Mori–Tanaka (MT) method. The values of the effective elastic properties of this composite are estimated in the presence of an interphase between the CNT and the polymer matrix which models the nonbonded van dar Waals interaction between the CNT and the polymer matrix. The effect of waviness of CNTs on the effective properties of the FFRC is investigated when the wavy CNTs are coplanar with two mutually orthogonal planes. The results demonstrate that the axial effective elastic properties of the FFRC containing wavy CNTs can be improved over those of the FFRC with straight CNTs.