When applying the uniform circular array to estimate arriving direction of wideband linear frequency modulation (LFM) signal, large amount of sampled points required to satisfy the Nyquist sampling theorem increases the burden of realtime processing system. In order to solve this problem, this paper puts forward and constructs a time difference direction finding model based on compressed sensing theory in small diameter circular array, and realizes the direction of arrival (DOA) estimation with fewer observation points. The results show that the proposed fractional time delay estimation method based on Compressed Sensing can achieve the same direction finding accuracy as the fractional time delay estimation algorithm for wideband LFM signals direction finding, and greatly reduces the computation load of data  and improves the time efficiency of the algorithm.