In this letter, we experimentally demonstrate multi-band linear frequency modulation (LFM) signal generation subjected to multi-input optical injection in an external cavity-based Fabry-Perot laser diode (ECFP-LD). The ECFP-LD is a specially designed FP-LD with a self-injected single longitudinal mode tuned up to 10 nm. The non-linear dynamics in period-one oscillation in ECFP-LD subjected to multi-input optical injection shows unique characteristics for multi-band linear frequency modulation. In the proposed scheme, four external input beams are injected to ECFP-LD, among which one is power modulated with the saw-tooth like waveform, and others are with the constant power. The varying power beam red-shifts the self-injected mode of ECFP-LD and mode-hopping on attaining a particular power level. Hence, multi-band LFM signals are generated by beating self-injected and multi-input injected beams with a large time-bandwidth product (TBWP). The total bandwidths of 12GHz (LFM1: 33-36 GHz, LFM2: 29-32 GHz, LFM3: 25-28 GHz, LFM4: 22-25 GHz) for four-band linear frequency modulation signals with a TBWP of 12000 is measured. The generated multi-band LFM signal provides flexibility on central frequency tunability and dynamic chirp rate for a multifunctional radar system.