In the presented paper, the free vibration of a polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness and surrounded by an elastic two-parameter foundation is analyzed. The shell is made of a polymeric matrix enriched simultaneously with randomly oriented carbon nanotubes (CNTs) and aligned glass fibers. CNTs agglomeration is included and the density and elastic constants of such a three-phase nanocomposite are calculated using the rule of mixture and the Eshelby–Mori–Tanaka approach alongside Hanh’s homogenization method. The conical shell and the elastic foundation are modeled using the first-order shear deformation theory and the Pasternak foundation model, consecutively. The governing equations are derived using Hamilton’s principle and are solved numerically via the differential quadrature method. The impacts of several parameters on the natural frequencies of such a structure are discussed such as thickness variation parameters, mass fraction and chirality of the CNTs, mass fraction of the fibers, and boundary conditions. It is observed that by considering the specific value for the average thickness of the shell, the thickness variation parameters associated with the highest natural frequency are different in various vibrational modes. It is discovered that the natural frequencies grow by increasing the mass fraction of the CNTs, but the influences of the mass fraction of the fibers on the natural frequencies are strongly dependent on the vibration mode.