A photonics-based anti-chromatic dispersion transmission scheme for multi-band linearly frequency modulated (LFM) signals is proposed and experimentally demonstrated. In the central station (CS), the key component is an integrated dual-polarization quadrature phase shift keying (DP-QPSK) modulator, of which the up-arm and down-arm are driven by a microwave reference signal and an intermediate-frequency (IF) LFM signal respectively. By properly adjusting the DP-QPSK modulator, optical frequency comb (OFC) and frequency shift lightwave are generated. After polarization coupling and remote transmission, the orthogonal-polarization optical signals are introduced into balanced photodetector for heterodyne detection. Thence, multi-band LFM signals are generated and transmitted to remote base stations (BS) with the largest power for the anti-chromatic dispersion ability. Experiments are conducted to verify the analysis. Multi-band LFM signals at L (1.5 GHz), C (7 GHz), X (10 GHz), Ku (15.5 GHz) and K (18.5 GHz) bands with flatness of 1.9 dB are simultaneously obtained in the CS after 50 km fiber transmission, while the normally double-sideband modulation approach experiences a significant power fading for the fiber dispersion. Tunability of the system is evaluated, and detection performances of the generated signals are also analyzed.