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In this paper, based on the viscoelastic theory, the creep buckling and post-buckling behaviors of a viscoelastic functionally graded material (FGM) cylindrical shell with initial deflection subjected to a uniform in-plane load are investigated. The material properties of the viscoelastic FGM cylindrical shell are assumed to vary through the structural thickness according to a power law distribution of the volume fraction of constituent materials and Poisson's ratio is assumed as a constant. Considering the transverse shear deformation and geometric nonlinearity, the constitutive relation of the viscoelastic FGM cylindrical shell is established. By means of the Newton-Newmark method and the Boltzmann superposition principle, the problem for the creep buckling and post-buckling of the FGM cylindrical shell is solved. The numerical results reveal that the transverse shear deformation, volume fraction and geometric parameters have significant effects on the creep buckling and post-buckling of the viscoelastic FGM cylindrical shell.