The evolution of cosine-super Gaussian (CSG) pulses propagating in a conventional single mode fiber (SMF) has been proposed. The propagation properties of CSG pulses are numerically studied by using split-step Fourier method, and the effects of initial phase φ₀ and order of the pulse m are analyzed. Results show that when φ₀ is increased to 80 rad, the first order CSG pulse will be compressed in a relatively long fiber, and then broaden monotonically; the higher order CSG pulses will experience a short compression first, and then broaden monotonically. In addition, the CSG pulses are compared with simple Gaussian pulses and Hyperbolic secant pulses. The results indicate that the Hyperbolic secant pulse broaden fastest; the simple Gaussian pulse broaden secondly; CSG pulses broaden slowest, which is most insensitive to the dispersion of fiber. The research work will pave a way to realize a special pulse in large-capacity, and long-range communications.