The dispersion of fiber Bragg gratings can be tunable by plating the nonuniform copper film of gradient thickness on the outer cladding of fiber grating along the axis and can be used as dynamic dispersion compensators. The fiber grating's dispersion is adjustable by changing the temperatures of the grating. A numerical model based on thermal balance equations has been used to analyze the dynamic characteristics of the nonuniform copper coated gratings. The reflection spectrum, time delay curve, and dispersion property were also analyzed for those gratings. The model has been verified by experiments.