This paper deals with mathematical modeling, design and application of Fiber Bragg Grating as temperature sensor .In this paper we used the MATLAB and filter characteristics simulation software as a tool for simulation results. The fabrication of Fiber Bragg Grating, their characteristics and fundamental properties are described. The reflectivity of FBG is described using simulation results. This paper also presents the simulation results of FBG as temperature and gas sensor. From the plotting analysis it can be concluded that for reduce the width of reflection spectrum we can take long grating.