Within the framework of effective-mass and envelope wave function approach, using a variational method, we have investigated the binding energy of shallow-donor impurities in an asymmetrical semiexponential quantum wells (ASEQW). The obtained numerical results show that the structure parameters (σ and, V 0) lead to significant changes in the impurity binding energy. Furthermore, these results show that the hydrogenic donor impurity binding energy may be increased or decreased as a function of the impurity position in quantum well.