•The dynamic model of an eccentric rotating CFRP cylindrical shell using FSDT is established for the first time.•The buckling and free vibration analyses of the eccentric rotating CFRP cylindrical shell are presented.•Taking into account the influences of coriolis and centrifugal forces caused by eccentric rotation.•The critical bucking mode of the shell alters from (1, 1) to (2, 1) with the increase of rotating speed. In this paper, the dynamic model of an eccentric rotating carbon fiber reinforced polymer (CFRP) laminated cylindrical shell based on the first-order shear deformation theory is established for the first time. The buckling and free vibration analyses of the eccentric rotating CFRP laminated cylindrical shell under the axial excitation are presented. Taking into account the influences of Coriolis force and centrifugal force caused by eccentric rotation. By utilizing the Hamilton principle, the first-order shear deformation theory and the von-Karman type nonlinear geometric relationship, a system of the partial differential governing equations for the eccentric rotating CFRP laminated cylindrical shell is derived. Then, the ordinary differential equations of the eccentric rotating CFRP laminated cylindrical shell are obtained according to Galerkin method. The present method are validated by carrying out some comparisons with the existing results in the published literatures. The natural frequencies and critical buckling loads of the system are solved numerically. In this study, the influences of the eccentric distance, ratio of radius to length, rotating speed as well as the number of layers of the eccentric rotating CFRP laminated cylindrical shell on the buckling and free vibration behaviors are discussed.