Aiming at a type of femtosecond optical solitary wave solution under arbitrary parameters discovered recently, the stability of the light pulse against some kinds of initial perturbations by employing numerical simulation is investigated. The results show that under the amplitude and wave shape perturbations the femtosecond pulse can propagate in a stable way and under the perturbations of random noise and chirp the light pulse can still propagate to a certain extension. These results will offer a theory support for the distortionless propagation of light pulse in optical fiber.