High speed communications and computations are the main industrial and academic demands. Optical method is one of amusing alternatives for doing this purpose 1.Fiber Optic communication provides higher frequency transmission of signals with greater bit rate and larger data carrying capacity over a long distance. This means of data transmission is with a lower loss and interference if compared to the normal copper wire used in the electrical telecommunication systems. Optical fiber is extensively used in the application of internet communication technology in developing countries widely due to its feasibility to transmit data over a longer distance 2.In spite of all these benefits this high speed optical fiber transmission system face an interruption in the form of GVD ,as different spectral components of the pulse travel at slightly different group velocities, a phenomenon referred to as GVD that limits the rates in optical transmission systems kanis 1-2. On the other hand, for long distance data transmission in optical fiber, nonlinear effects are introduced in the optical fiber that in turn limits the system performance 3kanis. SPM is one of the relevant nonlinear effects that dominate the system performance significantly kanis4-5. SPM effects observed when the Kerr non-linearity are the result of the pulses own intensity. The GVD which limits the rates in optical transmission systems are responsible for changes in pulse shape while SPM are responsible for changes of pulse spectrum. The combination of linear and nonlinear effects leads to both the temporal and spectral changes of the pulse 4-5.The pulse degradation in the fiber limits the maximum transmission distance and the transmission rate of the fiber link; hence it is very important to analyze the pulse behavior of the propagating pulse in the fiber 3. The pulse propagation is modeled using nonlinear Schrodinger equation (NLSE) 2. The chirp parameter, C have important role in pulse propagation. A chirp is a signal in which the frequency increases called up chirp (C>0) or decreases called down chirp (C>0) with time wiki. The effect of GVD is included through dispersion parameter that’s related to . If > 0, it is called normal dispersion regime while for < 0, it is called anomalous dispersion regime 8. In anomalous dispersion regime compression occurs for the up-chirped pulses, whereas the broadening takes place for the down-chirped pulses. The opposite situation happens for up- and down-chirped pulses propagating in the normal dispersion regime 4.In this paper, we investigate the change in pulse behavior for both up chirp & down chirp values by propagating a Gaussian pulse at normal and anomalous dispersion regime due to the effect of GVD. The non-linear effect SPM has been visualized for different propagation distance. Then we analyze the combined effect of SPM with GVD in both anomalous and normal regime. The results are compared for different cases. We used our numerical split step Fourier method for solving the pulse propagation equation numerically which takes account the effects of GVD and SPM.