The atomic structure and electronic properties of Cun nanoclusters (n = 4, 6, 7, and 10) supported on cubic nonpolar δ-MoC(001) and orthorhombic C- or Mo-terminated polar β-Mo2 C(001) surfaces have been investigated by means of periodic density functional theory based calculations. The electronic properties have been analyzed by means of the density of states, Bader charges, and electron localization function plots. The Cu nanoparticles supported on β-Mo2 C(001), either Mo- or C-terminated, tend to present a two-dimensional structure whereas a three-dimensional geometry is preferred when supported on δ-MoC(001), indicating that the Mo:C ratio and the surface polarity play a key role determining the structure of supported clusters. Nevertheless, calculations also reveal important differences between the C- and Mo-terminated β-Mo2 C(001) supports to the point that supported Cu particles exhibit different charge states, which opens a way to control the reactivity of these potential catalysts.