The modified nonlinear Schr?dinger equation and variational method are used to derive the evolution equations for the parameters of super-Gaussian pulse and their analytic solutions. The influence of the third-order dispersion on the propagation properties in different sharpness super-Gaussian pulses in optical fibers is discussed. Three restraint relations between amplitude and pulse width, pulse width and chirp, chirp and frequency and the center are derived. Analytical solution about the evolution of pulse-width versus propagation distance is obtained. By using Runge-Kutta algorithm, influence of the third-order dispersion and the degree of the pulse’s edge sharpness on the pulse-width is described. The results indicate that the amplitude and pulse width satisfy the adiabatic relation, when the dispersion coefficient increases to around 0.3 or the pulse sharpness coefficient m≥3, the pulse signal will obviously be stretched, its cycle will significantly be larger.