A novel photonic method is proposed to generate dual-band phase encoding linearly frequency modulation (LFM) waveforms. In this scheme, two binary sequences are sent into one dual-polarization Mach-Zehnder modulator (DPol-MZM) to perform phase modulation with the optical carrier, while driving LFM signal is sent into another DPol-MZM to generate second and fourth-order optical sidebands. Then, the generated sidebands and the phase modulated optical carrier are combined together to perform optical to electrical conversion. As a result, bandwidth doubled and quadrupled phase coded LFM signals can be produced. The proposed scheme is verified by simulation, dual-band signals of 6~10 GHz & 12~20 GHz, 6~13 GHz & 12~26 GHz and 8~10 GHz & 16~20 GHz are obtained by using 3~5 GHz, 3~6.5 GHz, and 4~5 GHz driving LFM signals, respectively. Furthermore, the applications of the generated dual-band signals on both radar and communication are demonstrated. For radar detection, optical de-chirping operation for the dual-band signals can be simultaneously realized by using a DPol-MZM, on the other hand, the time bandwidth product of the radar waveform can be improved by phase encoding the LFM signal with M sequence. For wireless communication, each band LFM signal can be modulated with a binary sequence, and the two phase-coded LFM signals can be coherently demodulated in the optical domain. The proposed method features multi-functional operation, which can be potentially employed in radar-communication integrated systems.