Photonic-based dual-chirp microwave waveform generation with multi-carrier frequencies and large time-bandwidth product (TBWP) is proposed. In the approach, a polarization modulator is employed to introduce parabolic phase difference into the injected optical signals. After heterodyne detection in balanced photodetector, dual-chirp microwave waveforms with multi-carrier frequencies are generated. To remedy the TBWP limitation, approach based on splitting parabolic waveform is employed to increase the bandwidth of the generated waveforms while controlling the temporal duration unchanged. The generator features multi-band generation ability and large TBWP performance. Simulations show that bandwidth of the generated signals are increased by N/2 times after splitting the parabolic waveform into N pieces. Four-band dual-chirp signals with bandwidth of 7.32 GHz and TWBP of 6000 are generated. Auto-correlations of the generated waveforms exhibit good pulse compression performance. Ambiguity functions of the generated signals are analyzed, polarization offsets and approach limitations are also investigated.