A photonic method for multi-band linearly frequency-modulated (LFM) signal generation is proposed and demonstrated experimentally. An intermediate-frequency (IF) LFM signal and a single-tone radio frequency (RF) signal are first coupled by an electrical coupler. Then the coupling signal is used to drive a single-drive Mach–Zehnder modulator (SDMZM). By properly setting the frequencies and corresponding modulation indices of the IF LFM signal and RF signal, the multi-band LFM signal can be generated. The number of sub-bands can be adjusted by simply controlling the direct current bias of the SDMZM. The proposed method features simple structure and flexible tunability, which is promising for modern multi-band radar systems.