Based on Eringen’s nonlocal linear elastic theory and n-th order generalized beam theory (GBT), the coupled vibration and buckling characteristics of functionally graded material (FGM) nanobeams subjected to thermal-mechanical loads were investigated by using a modified generalized differential quadrature (MGDQ) method.The material properties were temperature-dependent according to the Voigt mixture power-law model and various types of temperature distributions were assumed to be steady along the thickness direction of the structure.The governing differential equations for the coupled vibration and buckling of the system were derived unifiedly in accordance with the Hamilton’s principle.By introducing control parameters for three different kinds of boundary conditions, the MGDQ method was  used to solve the coupled vibration response of the structure with the MATLAB procedure.A loop subprogram was also written to obtain the static responses based on the duality between the vibration and buckling responses of FGM nanobeams.The MGDQ method presented was validated to be available and highly efficient by comparison with those of available results in the literature.Finally, the effects of various beam theories, boundary conditions, nonlocal scale parameters, initial axial mechanical loads, various types of temperature distributions, temperature rises, thermal-mechanical loads, material graded index and slenderness ratios on the vibration and buckling characteristics of FGM nanobeams were studied.