The spectro-geometric method is utilized to investigate the free and transient vibration characteristics of the functionally graded （FG） cylindrical shell under thermal environment. The boundary restraining spring technology is employed to simulate the arbitrary classical or elastic boundary support of the shell structure. The energy functional of FG cylindrical shell under thermal environment is established with the first-order shear shell theory. The displacement admissible functions of the cylindrical shell are characterized by the spectro-geometric method and circumferential Fourier harmonic function product sum to overcome the discontinuity problem of the shell boundary displacement function differential along the boundary edge of the shell structure. By substituting the displacement admissible function into the cylindrical shell energy functional， the Ritz approach is employed to construct the vibration analysis model. The numerical analysis results show that the current model can predict the vibration characteristics of FG cylindrical shells with high precision. The influence of power law exponents， thermal environment and load parameters on the vibration characteristics of FG cylindrical shells is studied. The new results presented in this study can be utilized as benchmark solution for other numerical method development.