Abstract: Intermediate frequency (IF) echo of broadband radar is sparse in frequency domain. According to compressed sensing theory, compressive sampling can be applied to the IF echo and original signal can be reconstructed from compressive sample with high probability. In the reconstruction of compressive sample for IF echo, the dimensions of the needed matrix are determined by the length of the echo. In case the IF echo is with long duration, the dimensions of the matrix are large, much more memory resources are occupied and the processing speed is slow. In order to solve this problem, stagewise overlap processing is introduced into the reconstruction. Firstly, reconstruction method with stagewise overlap processing is described detailedly,. Then through strictly mathematical deduction, it is proved that the connection between spectrum leakage and local time domain sequence is with a characteristic. The characteristic is that the influence by the two ends of time sequence on the value of spectrum which is close to the spectrum peak is larger than it on the value of spectrum which is away from the spectrum peak. Utilzing the characteristic, the mechanism of restraining error for stagewise overlap processing is illustrated. Experiment with real data indicates that the stagewise overlap processing has better reconstruction quality than reconstruction method with stagewise but no overlap and the stagewise overlap processing need less memory resources than holistic reconstruction method which deals with the pulse as a whole.