A method for photonic generation of a linearly chirped microwave waveform using a frequency-sweeping laser and a dual-polarization modulator is proposed and investigated. A frequency-sweeping continuous-wave light is generated from the laser and then sent to the modulator. In the modulator, one part of the light is modulated with an RF signal to generate a frequency-shifting optical signal, while another part of the light is passed through a polarization rotator to rotate the polarization to an orthogonal direction. At the output of the modulator, the two optical signals are combined with orthogonal polarizations, and then injected into a polarization delay device to introduce a time delay. After combining the two optical signals for heterodyning, a linearly chirped waveform can be generated. The bandwidth, time duration, chirp rate and sign, central frequency of the generated waveform can be tuned independently and flexibly, furthermore, frequency doubling for the central frequency can be achieved in the waveform generation. A simulation is demonstrated to verify the proposed scheme, a linearly chirped microwave pulse with up or down chirp, central frequency of 20 or 40 GHz, bandwidth of 20 GHz, time duration of 500 ns, time-bandwidth product (TBWP) of 10000 is obtained.