We have calculated the binding energies of the donor states, 1s and 2p +/-, with respect to the lowest sub-band energy in a double quantum well composed of wurtzite InGaN staggered quantum wells with GaN barriers. All the energies and the wavefunctions were calculated by applying the variational methods. We have found that the binding energies of donors placed in the right quantum well are larger and independent of the middle barrier width of up to 40 angstrom. This is because of the strong built-in electric field which brings more confinement to the donor wavefunctions in the right staggered quantum well. The binding energies are found to be strong functions of the donor position in the double quantum well system which is the consequence of the large asymmetry introduced by the built-in electric field.