Using the method of matrix diagonalization, we investigate an off-center D~- in a spherical quantum dot(QD) subjected to a parabolic potential confinement. We discuss the effect of the position of an impurity in the QD onthe binding energy of the D~- system. Furthermore, we compare a negatively charged donor D~- with a neutral donorD~0 confined by a spherical QD with a parabolic potential. The results have clearly demonstrate the so-called quantumsize effect. The binding energy is dependent on the confining potential hω_0 and the impurity ion distance D. Using the method of matrix diagonalization, we investigate an off-center D ~ - in a spherical quantum dot (QD) subjected to a parabolic potential confinement. We discuss the effect of the position of an impurity in the QD on the binding energy of the D ~ - system. Furthermore, we compare a negatively charged donor D ~ - with a neutral donor D ~ 0 confined by a spherical QD with a parabolic potential. The results have clearly demonstrated the so-called quantumsize effect. The binding energy is dependent on the confining potential hω_0 and the impurity ion distance D.