In this work, the electronic structure and the inter-subband absorption coefficient (IAC) are theoretically studied for symmetric double n-type delta-doped GaAs quantum well considering the donor impurity atom effect. The electron states are determined by a diagonalization procedure, working within the effective mass and parabolic band approximations, and the effect of donor center is treated via the variational method. Meanwhile, linear and nonlinear contributions for the inter-subband absorption coefficient were evaluated from expressions usually derived within the perturbative solution of the Von Neumann equation for density matrix. We report the impurity binding energy by considering a donor atom located at the center of the system (at z(i) = 0). We found that the reported physical properties become more sensitive to the inter-well separation distance L-w than to the delta-doping density, N-2d. In the former case the total optical absorption coefficient undergoes an important red-shift as well as a significant decrease in its magnitude. When N-2d values increase, the binding energy exhibits a contrary effect, and the total optical absorption coefficient exhibits an small blue-shift with no significant changes in its magnitude. The presence of the donor impurity atom in the system represents one factor that can modify the location of inter-subband absorption coefficient, by inducing a blue-shift of the optical response. The resonant peak energies are within the range of several terahertz, showing potential device applications within this range of the electromagnetic spectrum.