In the present work, x-ray powder diffraction patten (XRD) of scandium metallic nanoparticles with hexagonal crystal structure is computationally simulated. To do this, the original formulation of light diffraction which is very more general than the Bragg diffraction relation, is used in a home-made computer code. The results of the simulation are that for nanoparticles with sizes larger than 20 nanometers, the pattern has no differences (expect for some peak heights) with the bulk crystal, but, for sizes smaller than 10 nm, the pattern shape and especially the peaks width strongly will depend on the nanoparticle size.