For a quantum well which has the Tietz-Hua potential, the ground and some excited donor impurity binding energies and the total absorption coefficients, including linear and third order nonlinear terms for the transitions between the related impurity states with respect to the structure parameters and the impurity position as well as the electric field strength are investigated. The binding energies were obtained using the effective-mass approximation within a variational scheme and the optical transitions between any two impurity states were calculated by using the density matrix formalism and the perturbation expansion method. Our results show that the effects of the electric field and the structure parameters on the optical transitions are more pronounced. So we can adjust the red or blue shift in the peak position of the absorption coefficient by changing the strength of the electric field as well as the structure parameters. (C) 2017 Elsevier B.V. All rights reserved.