The nonlinear propagation characteristics of exponential optical pulses with initial linear frequency chirps in an anoma-lous-dispersion single mode fiber are numerically studied and compared with those of hyperbolic secant pulses.The effect of the negative chirp on pulse broadening is greater than that of the positive chirp when pulse amplitudeA =1 and the exponential pulse is more sensitive to the impact of the chirp than the hyperbolic secant pulse.WhenA >1.2

the pulse width oscillates in a periodically damped manner with the propagating distance and the period and amplitude of the oscillation increase with the in-crease of chirp parameter| C |when| C |≤2.The exponential pulse finally evolves into an optical soliton and the minimal value Arequired for this evolution is larger than that of hyperbolic secant pulse.