Metal nanoalloys on oxide surface are a widely studied topic in surface science and technology. In this study, the structures of CoPd nanoalloys adsorbed on MgO(001) have been searched by basin-hopping global optimization method within an atomistic model. Two different sizes (34 and 38 atom) have been considered for all compositions of CoPd/MgO(001) nanoalloys. Co and Pd atoms, for all the compositions, have cube-on-cube (001) epitaxy with substrate at interface. For both sizes, we have found that Pd rich composition nanoalloys have three layers, Co rich composition nanoalloys have four layers in morphology. Excess energy and second difference in energy analyzes have been performed to investigate the relative stability of nanoalloys with respect to their size and composition.