We have studied the electronic properties in presence of an off-center hydrogenic shallow donor impurity confined in GaAs semiconductor quantum dot with toroidal geometry by considering the infinite confinement potential. This study has been performed within the parabolic band and the effective mass approximations in the presence of an off-center donor impurity. Three-dimensional Schrödinger equations are discretized using the finite difference method on a mesh containing N r *N θ *N φ nodes. The numerical results of the analytical calculations demonstrate that the variation of the geometrical and torus radii (R g and R c ) has a remarkable effect on the donor energy and the average electron-impurity distance, which is quite remarkable in small hemi-Toroidal quantum dot. On the other hand, we've demonstrated that the donor atom's position has a considerable impact on their energy. Furthermore, our numerical results show that the geometrical radius and donor atom's position significantly affect the electron impurity binding energy.