In this paper, we propose an approach to generate microwave pulses with wide frequency multiplication tuning range based on the unbalanced temporal pulse shaping (TPS) principle. The key to achieving a wide tuning range is a linearly chirped fiber Bragg grating (LCFBG) with programmable dispersion which is incorporated in an unbalanced TPS system. We experimentally demonstrate generation of microwave pulses whose centre frequency can be tuned from 3.7 GHz to 9.2 GHz.