A photonic approach to realizing anti-chromatic dispersion transmission for a frequency and bandwidth-doubling dual-chirp microwave waveform is proposed and experimentally demonstrated. The system has no requirement on polarization devices or optical filters for only the integrated dual-drive dual-parallel Mach-Zehnder modulator employed. To overcome chromatic dispersion, the carrier frequency suppression approach is proposed. The anti-chromatic dispersion process is accomplished in a central station and independent to carrier frequency, fiber length, and dispersion coefficients. An experiment is conducted to verify the analysis. Dual-chirp waveforms at 13 GHz with a bandwidth of 0.8 GHz and time duration of 1 μs are obtained. After 25 km fiber transmission, the proposed approach shows a relatively flat curve in a frequency-power diagram, while the normally carrier-suppressed double-sideband modulation method experiences a significant power fading for fiber dispersion.