Optical fiber is one of the most important communications media in communication system. Due to its versatile advantages and negligible transmission loss it is used in high speed data transmission. Although optical fiber communication has a lot of advantages, dispersion is the main performance limiting factor. Dispersion severely degrades the performance of optical fiber. There are various methods for dispersion compensation. Due to some superior advantages Fiber Bragg Grating is a well known hot cake in the field of dispersion compensation in optical fiber communication. Generally Fiber Bragg Grating has a very narrow operating window. An effective method for broadening the window of Fiber Bragg grating is shown in this thesis work, which gives a satisfactory operating window. In this thesis paper a typical MATLAB simulation work is done to compensate dispersion up to a fiber length of 300 Km.