In the low-saturation limit, the property of atomic absorption resulted from the interaction between coherent light and N-type four-level system is investigated. With the numerical method, the influences of the offset of stronger light, probe-field strength and branching ratio coefficient of spontaneous decay from excited level to lower levels to atomic absorption are discussed. The results exhibit that the coupling offset makes the atomic absorption modified in transverse orientation, and the signal offset in vertical orientation; the probe-field strength modifies the nonlinear absorption which modifies the atomic absorption, it is found that when the strength of the probe-field is far less than that of the coupling and signal field the atomic absorption is the same as the linear absorption, and it shows the characteristic of electromagnetically induced transparency; when the probe field strength continues to increase the gain emerges in the nonlinear absorption, and the atomic absorption begins to change from the transparency window to the gain one; as is known, an excited level in the system decays to two lower levels. When the branching ratio coefficient corresponding to the probe channel is near to zero, a rapid variety emerges in the atomic absorption, and when the branching ratio coefficient is equal to zero, the gain in the atomic absorption becomes infinite on the resonance of the probe field.