The single wurtzite Zn1-xCdxO/ZnO quantum well structure in polar c-direction is studied and the binding energies of an impurity donor atom are obtained. The Schrodinger and Poisson equations are solved self consistently using finite difference method within the effective mass and envelope function approximations. Then, a hydrogenic type of wave function is assumed to represent the impurity, and donor binding energies are obtained using variational approach. The binding energies of the 1s and 2p(+/-) states and the transition energy between them are obtained as functions well width, Cd concentration and donor position in the well. Also, an external magnetic field along the growth direction up to 10 T is applied to compute the changes in the binding energies. The builtin electric field causes an asymmetric band profile and a triangular well structure, and makes the binding energy curves lose symmetry. The binding energy increases with the donor position as the donor gets close to the wave function penetrated mostly inside the barrier. The built-in electric field is 2.5 MV /cm in a 20- angstrom well with the Cd concentration of x = 0.1, and the transition energy is 27.7 meV (6.7 THz) when the donor is at the well barrier interface close to the electron wave function, but it is 15.7 meV (3.8 THz) when the donor is at the well center. Also, the Zeeman splitting between the 2p(-) and 2p(+) states is 4.64 meV at 10 T independent from the donor position.