Aiming at the problem that traditional methods cannot estimate the bandwidth of under-sampled Linear Frequency Modulation(LFM) signals under low Signal Noise Ratio(SNR), a bandwidth estimation method based on Distributed Compressive Sensing(DCS) is proposed, which uses the joint sparse characteristics of multiple LFM signals with the same modulation type from the same source to estimate the bandwidth of LFM signal. Firstly, the under-sampled LFM signal model is constructed. Secondly, the LFM bandwidth is reconstructed by DCS algorithm. Then the parameter estimation ability of the proposed method under low SNR conditions is analyzed. Finally, the feasibility and validity of the proposed method are verified by simulation.