In this paper, nonlinear vibrations of fiber-reinforced composite cylindrical shells (FRCCSs) with bolted joint boundary conditions are studied both theoretically and experimentally, where the nonlinear amplitude-dependent material property of fiber-reinforce composites (FRCs) and partial bolt loosening boundary conditions are taken into account. By representing the nonlinear material property via Jones-Nelson theory, Love shell theory is used to calculate the elastic strain energy of shells. The bolt loosening boundary conditions are achieved using artificial spring-damper technique. The Rayleigh-Ritz method is employed to derive the equations of motion for FRCCSs, from which the natural frequencies, damping ratios, and forced response can be obtained. Then, a series of vibration tests are carried out on a FRCCS specimen to validate the modeling approach proposed here. Based on the validated model, vibrations of FRCCS structures accounting for amplitude dependence of FRCs with different partial bolt loosening boundary conditions are investigated. It is found that increasing bolt loosening degree and loose bolt number leads to decrement of natural frequencies, and increment of modal damping ratios and resonant response amplitudes due to the coupling effect of declined boundary stiffness and increased boundary damping at bolted constraint edges. As the excitation level rises, the amplitude-dependent characteristics of natural frequencies and damping parameters of FRCCSs gradually become weak, while the increasing rates of resonant response amplitudes show an upward trend.