An analytic expression of the self-phase modulation induced by chirp in non-Kerr-like optical fibers with saturable nonlinearity is derived taking into account the fiber loss. The evolution of chirp is simulated by computer. The results show that the more powerful the saturable effects, the smaller the chirp induced by self-phase modulation; the chirp increases in magnitude with the propagation distance and the chirp depends on the fiber loss and the peak power of the incident pulse.