Linearly frequency modulated (LFM) microwave signals have received extensive attention due to their better improved target detection capability. A photonic-assisted chirp microwave waveform generation scheme with switchable bands is proposed based on a dual-polarization dual-parallel Mach-Zehnder modulator (DP-DPMZM). A radio frequency (RF) signal and a baseband linearly frequency modulated (LFM) signal are applied on DPMZMX and DPMZMY, respectively.For the generation of LFM signal at one band, both DPMZMX and DPMZMY are biased to achieve carrier suppressed single sideband modulation (CS-SSB). When changing the phase shift between the two RF signals and the bias voltages applied on the DPMZMX, the +2 nd -order sideband and optical carrier are obtained at X polarization. Meanwhile, DPMZMY is biased to achieve single sideband (SSB) modulation at Y polarization. Thanks to the polarization property of optical signal, the optical carrier can be cancelled, thus a LFM signal at another band can be generated. An experiment is conducted to validate the proposed scheme. Experimental results show that down-chirped LFM signals at X-band and K-band are obtained. Since SSB modulation is adopted for the system, the dispersion-induced power fading can be eliminated. The proposed scheme has wide applications in multi-target and long-distance detection in radar systems.