Purpose: Free vibrations of non-homogenous (functionally graded material (FGM)) axisymmetric nonlocal thermoelastic hollow sphere has been taken into consideration for investigation. The material of nonlocal thermoelastic sphere is supposed to be graded using power law in radial direction. Methods: The solution of continued power series is employed to resolve the differential equations and to investigate the analytical solutions for field functions i.e. temperature, stress and displacement. Results and Conclusions: The analytical results have been authenticated using numerical computations with computer based software like MATLAB. The numerical results have been shown graphically for the comparison of frequency shift and thermoelastic damping for local and nonlocal elastic materials. Deduction of results has been validated with the already published literature. © 2020, Krishtel eMaging Solutions Private Limited.