The present article deals with the vibration and damping analysis of functionally graded carbon nanotubes reinforced hybrid composite (FG-CNTRHC) shell structure which consists of conventional carbon fiber as reinforcing phase and single-walled carbon nanotubes based polymer as matrix phase. The Eshelby-Mori-Tanaka approach in conjunction with strength of material approach is implemented to obtain the material properties of FG-CNTRHC structures. The material properties of FG-CNTRHCs are assumed to be graded through the thickness direction according to power law distributions of the volume fraction of carbon fibers and fiber orientations. An eight node shell element considering transverse shear effect according to Mindlin's hypothesis has been formulated for finite element modelling and analysis of such functionally graded hybrid composite shell structures. The formulation of shell midsurface in an arbitrary curvilinear coordinate system based on the tensorial notation also presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on damping capacity of such hybrid shell structures. Different types of spherical shell panels have been analyzed in order to study the time and frequency responses. The influences of CNTs, carbon fiber, geometry of the shell, power law index and material distributions on the vibration damping characteristics of FG-CNTRHC shell structures have also been presented and discussed. Various types of FG-CNTRHC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to comparative studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency and the effects of CNTs on vibrations responses of such shell structures are also presented. © 2017 SAGE Publications.