  We numerically study the ground state properties of endohedrally confined
hydrogen (H) or helium (He) atom by a molecule of C$_{60}$. Our study is based
on Diffusion Monte Carlo method. We calculate the effects of centered and small
off-centered H- or He-atom on the ground state properties of the systems and
describe the variation of ground state energies due to the C$_{60}$ parameters
and the confined atomic nuclei positions. Finally, we calculate the electron
distributions in $x-z$ plane in a wide range of C$_{60}$ parameters.
