The binding energy of the ground state of a hydrogenic off-center donor in a spherical quantum dot under a parabolic potential is calculated by a variational method within the effective-mass approximation. The parabolic potential is assumed to be a spherically symmetric potential. The location effects of a hydrogenic donor under a parabolic potential on the binding energy of the ground state are studied. It is found that in the case of an on-center donor, the parabolic potential tends to enhance the strength of the Coulomb interaction and the binding energy of the ground state, and in the case of an off-center donor, the effect of the parabolic potential on the binding energy of the ground state is somewhat complicated.