Abstract: Compressive sensing technology is used to realize fast sub-Nyquist sampling process of wideband signal, wideband LFM pulse compress radar can resolved conflict between radar range and radar range discrimination effectively and is applied in the detecting field. The research of signal sparse decomposition and reconstruction algorithm are carried out firstly for the fast sub-Nyquist sampling process of wideband LFM pulse compress radar signal. OMP algorithm which has some characteristics such as rapid operating rate and high reconstructive precision is picked up among greedy algorithm, protruding relaxation algorithm and combination algorithm. Then OMP algorithm is carried out in the compressive sensing simulation analysis of wideband LFM pulse compress radar signal. It is showed by simulated conclusion that OMP algorithm can be used to complete sub-Nyquist sampling and reconstruction of wideband LFM pulse compress radar signal under higher SNR condition, which will offer better theoretical guidance for the processing problem of super wideband radar signal.