Based on a spherical shell structure and the graded finite potential well model,shifts of bound states caused by the interface effects on the binding energy level of hydrogenic impurities in a weakly-confined spherical semiconductor quantum dot heterostructures are studied. It is found that the interface effects are fairly significant when the shell thickness of the quantum dot is less than or equal to 10 nm. The interface effects become weaker when the thickness of the heterostructures increass,and the ground state energies gradually decrease. Finally the ground state energies corresponding to different values when Aity function becomes zero tend to be a fixed value,then the interface effects can be ignored.