Projection Onto Convex Sets (POCS) is an iterative method to obtain the information from one domain using the information available in other domains, and it has been widely used in image restoration problems and block-based DCT compression standards as a post-processing scheme. In this paper, we study an iterative signal reconstruction method for signal reconstruction and sparse signal compression. This method is similar to POCS method. From known partial time-domain samples and partial frequency-domain coefficients, it iteratively projects the signal onto the known samplespsila subspaces and the known coefficientspsila subspaces. Finally the signal can recover closely by using this iterative reconstruction scheme. Some experiments show this method can correctly and effectively reconstruct the underlying signals.