By using the compact density matrix approach, the linear and nonlinear optical absorption coefficients in a GaN-based step quantum well (QW) with strong built-in electric field (BEF) have been theoretically deduced and investigated in detail. The band nonparabolicity is taken into account by using an energy-dependent effective mass (EDEM) method. The exact electronic eigen-states in the step QW with strong BEF were obtained and the simple analytical formulas for the linear and nonlinear optical absorption coefficients in the systems were also deduced. Numerical calculations on an AlN/GaN/AlxGa1-xN/AlN step QW were performed. It is found that the decreasing of well width Lw and step barrier width Lb and the doped concentration x in step barrier can result in the enhancement of the absorption coefficients. Moreover, with the decrease of Lw, Lb and x, the photon energies of absorption have blue-shift, and the full-width-at-half-maximum of the total absorption coefficient increases and the saturation absorption intensity decrease. Some results are consistent with recent experimental observations.