According to the analysis of gain theory, the absorption or gain of medium depends on pump power. The coherent population oscillation leads the pulse to experience absorption saturation and propagation delay in a medium with absorption. This effect induces the pulse to experience gain saturation and propagation advance in a medium with gain. Making use of the transition rate equation of metastable state poplation, we develop the model of fast light in erbium-doped optical fiber and obtain the analytic expression of time advance. We demonstrate that there is a saturation effect of fast light in low frequency region, but the fast light is enhanced with pump power increasing in high frequency region.