Analytic expression for the linear and third-order nonlinear optical absorption coefficients was obtained in square tangent quantum well by the compact density-matrix method and the iterative procedure. The numerical results for typical GaAs/AlGaAs material show that the well width b, well depth V0 and incident intensity I have great influence on the absorption coefficients and the total optical absorption coefficients are induced with the enhancement of b and the reduction of V0. It is obtained that the peak absorption shift to the aspect of the low energy. Moreover, the peak of the total optical absorption coefficients is significantly induced and the strong absorption saturation will occur with increasing of the incident intensity.