Abstract: Compressive sensing (CS) theory is highly focused in radar community over the last decade. Its incoherence measurement process can effectively reduce the data rate of high-resolution imaging radar system. Consequently, compressive sensing theory can be used to release the burden of radar system on huge amount of data sampling, storage and transmission. This paper concentrates on finding a kind of proper reconstruction algorithm when dealing with the radar echo with compressive sensing theory. The broadband radar echo has a sparse representation on the amplitude-delay sparse dictionary. Compressive sensing theory can greatly reduce the amount of data through dimension reduction sampling based on this feature. After the dimension reduction sampling, we need to find a proper algorithm to reconstruct the original signal. In order to solve this problem, a kind of sparse iterative covariance-based estimation method (SPICE) is studied in this paper. SPICE is computationally quite efficient and enjoys global convergence properties. Besides, this algorithm does not require any subtle choices of user parameters and can be used in many fields, such as spectral analysis, array processing, astronautic applications and so on. In this paper, we apply this algorithm to wide-band radar, which is widely used in both military and civil fields. During the simulation, an amplitude-delay sparse dictionary was constructed according to the characteristics of the radar echo signal waveform firstly. Then, the amount of data was compressed through random sampling. Finally, SPICE, as the signal reconstruction algorithm, was introduced into the process of the radar echo based on compressive sensing theory. The simulation results show that the usage of SPICE parameter estimation makes the degree of compression ratio very small and the relative error between reconstruction signal and original signal is also small. In addition, the SPICE algorithm itself has data adaptive features, which is an important advantage different from other kinds of algorithm. As a consequence, there is no need to select end conditions according to the signal feature. At the same time, the algorithm also converges very fast, and can estimate the sparse parameters of radar echoes in a relatively short period of time. This advantage can meet the requirement of real-time for wide-band radar target detection.