In the n-type four-level atomic system, we have studied the nonlinear theory of electromagnetically induced absorption. The results show that the probe light Rabi frequency and the attenuation distribution coefficient A affect the nonlinear absorption and then the absorption of a medium. When the probe light intensity is weak, the absorption of the medium and the linear absorption are the same, showing the characteristics of electromagnetic induction absorption. When the probe light intensity is increased, the absorption of the medium and the linear absorption are no longer the same, and now the medium absorption curve will show hole burning phenomenon, and then it will show the gain phenomenon. At the same time, the nonlinear absorption is affected by the value of A. Even if the probe light is weak, the medium absorption will change the electromagnetic induction absorption into the gain phenomenon with the A value decreasing.