We have calculated the ground and excited energy states of the quantum dot as a function of the depth of confining potential well and radius R. Based on the calculated energies and wave functions, the electric field gradient induced by the non-spherical charge at impurity is investigated as a function of dot radius and the confining potential. For Deuterium dot with spherical confining potential, the expectation value of the quadrupole moment operator is carried out. The calculations show that the dot radius, the confining potential and the impurity charge have a great influence on the electric field gradient and the quadrupole moment. It is found that as the confining potential increases, the peak position of the electric field gradient shifts toward smaller dot radii and its amplitude increases with the increase of confining potential.