High-resolution compressive sensing imaging with stepped-frequency noise signal (SFNS) is presented. The SFNS is similar to the stepped - frequency chirp signal (SFCS), which is also composed of a burst of subpulses with their carrier frequencies linearly increased or decreased, but each subpulse is a noise signal instead of a chirp signal. The noise signal of each subpulse is realized by Logistic mapping, i.e. it is a kind of chaotic signal or random like signal. Range compression for SFNS can be as same as that for SFCS when matched filtering (MF) is used. However when the compressive sensing (CS) approach is used, they are quite different. As for SFCS random sampling is performed to echoes of the subchirps while evenly sampling is performed for SFNS. Real data from a moving train is processed to demonstrate the effectiveness of both the signal model and the CS imaging algorithm.