A method is proposed to extend the dynamic strain range of fiber-optic distributed sensing based on linear frequency modulation (LFM) pulse sideband modulation. Based on inverse ratio between the frequency-modulated bandwidth and the coherent time-domain signal envelope shift, multiple modulated sidebands with different frequency-modulated bandwidths are generated in a single pulse for sensing. Coherent time-domain signals of each sideband are digitally band-pass filtered and decomposed to achieve simultaneous measurements of events with different dynamic strain ranges. LFM signals with frequency modulated bandwidths of 40 MHz and 200 MHz are used to modulate sidebands in experiments, respectively. The results show that the system can simultaneously measure the maximum amplitude of 7 nε and 350 nε sinusoidal dynamic strain events, which provides a dynamic range expansion scheme for fiber-optic distributed acoustic sensor system.