In the present theoretical study, the linear and third-order nonlinear optical absorption coefficients have been calculated in GaAs/Ga1−xAlxAs inverse parabolic quantum wells (single and double) subjected to an external electric field. Our calculations are based on the potential morphing method in the effective mass approximation. The systematic theoretical investigation contains results with all possible combinations of the involved parameters, as quantum well width, quantum barrier width, Al concentration at each well center and magnitude of the external electric field. Our results indicate that in most cases investigated, the increase of the electric field blue-shifts the peak positions of the total absorption coefficient. In all cases studied it became apparent that the incident optical intensity considerably affects the total absorption coefficient.