Within the framework of effective mass approximation, the binding energy of a hydrogenic donor impurity in Gax In1-x Asy P1-y stepped quantum wells (SQWs) is theoretically calculated using the variational method. The influence of applied electric fields and SQWs height on hydrogenic donor impurity electronic state is investigated. The results show that the hydrogen impurity binding energy reaches its maximum when the donor impurity is located at the center of the stepped quantum wells. The applied electric fields drive the electron wave function away from the stepped quantum well center, and induce asymmetric distribution of the donor binding energy in the SQWs. The variation of Ga and As content leads to the corresponding changes in the stepped quantum well height, which significantly affects the binding energy of hydrogenic impurities in the stepped quantum wells. The results are meaningful and can be applied in the design of optoelectronic devices based on stepped quantum wells.