In active fiber two kinds of nonlinearity, nonlinear polarization and gain saturation, laed to the frequency spectrum broadening of optical signal. Gain saturation distorts its envelope, and affects the self-phase-modulation (SPM) caused by nonlinear polarization. It can be expressed by a transmission function f(z). A formula of f(z) with a power series derived from NLS equation is given, and the frequency broad band can be estimated by B=2F(1+μ). Because of f(z)>>1 in the active fiber, the broadening can be compared with initial band of optical signal in the optical communication system having many optical fiber amplifiers with high gain and high output power.