In this work, a non-local finite-element formulation is developed to analyse free vibration of functionally graded (FG) nanobeams considering power-law variation of material through thickness of the nanobeam. The Euler Bernoulli beam theory based on Eringen's non-local elasticity theory with one length scale parameter is used to model the FG nanobeam. To this end, two types of FG nanobeams composed of two different materials are analysed by using the developed non-local finite-element formulation. First FG nanobeam is made of alumina (Al2O3) and steel, whereas second one is composed of silicon carbide (SiC) and stainless steel (SUS304). Numerical results are presented to show the effect of power-law exponent (k) and nanostructural length scale (e(0)a/L) on the free vibration of FG nanobeams.