The fundamental issue limiting long-distance and high-speed optical fiber transmission is dispersion. Dispersion impairs system performance, the signal-to-noise ratio (SNR), and the bit error rate (BER). To address this, numerous dispersion modification techniques have been developed. The use of fiber Bragg grating (FBG) is one of the efficient strategies for dispersion compensation. The FBG is frequently used as a filter. The proposed model uses uniform fiber Bragg grating UFBG. Two cascaded FBGs with varying lengths, a constant grating period, and a constant spacing between FBGs are employed in the proposed thesis. The input signal for the stage that follows is the output signal from the previous stage. The best performance and many applications are considered while modeling, analyzing, and comparing this system. Transmission and reflection in two cascaded stages of fiber Bragg grating using first and second order are studied. The mathematical equations for the proposed model are simulated in MATLAB.