Abstract: Random noise radar executes pulse compression via direct correlation in time domain for target detection. A novel algorithm is proposed based on compressive sensing for random noise radar system. Projection for low dimension data is adopted instead of correlation; Signal reconstruction is used to substitute signal compression; And much computational load is transferred to background processing. In this algorithm, detected targets in scene satisfy the requirement of sparsity peculiarity, and measurement matrix is constructed by selecting the rows of convolution matrix stochastically. Furthermore, two step iterative shrinkage/thresholding algorithm is applied to reconstruct target signals. With elaborate theoretical derivation, the whole processing of this algorithm is presented. Simulation results are provided to show that the algorithm is able to reconstruct targets efficiently with well computational efficiency. Moreover, factors highly influencing on the results are analyzed. In contrast to correlation operation, reconstruction error is significantly reduced and sidelobes are faithfully suppressed. In addition, phase characters of target information are preserved well.