An analytic expression is obtained for the chirp induced by the dispersion in the stepwise decreasing dispersion fiber. Using numerical method, we simulate the evolution of chirp in the stepwise decreasing dispersion fiber. The results show that the chirp in the stepwise decreasing dispersion fiber varies jumply taking the chirp in the fiber of slowly decreasing dispersion as the centre at the beginning, then the chirps coincide gradually with each other. However the chirp in the stepwise-descreasing-despersion fiber is smaller than the chirp in the conventional fiber.