A photonic approach to generating chirped microwave signal with high time-bandwidth product (TBWP) is proposed. The scheme utilizes the linear frequency-to-time mapping of a spectrally-shaped optical pulse propagating through a dispersive element. A mode-locked laser for generating short optical pulses and a programmable optical filter (POF) to shape the spectrum of the pulses are employed. Experiment results show that the chirped signal with a TBWP and compression ratio both in excess of 60 is achieved. We also estimate theoretically the maximum TBWP that can be achieved over 300 under the constraint of the finite frequency resolution of the applied POF. The effect of higher order dispersion on the generated RF pulses and the TBWP is also investigated.