Traditional multi-frequency radar signal fusion can reconstruct full-band signal from some continuous sampled sub-band signals, and can improve range resolution and quality of range profile. But by the theory of Compressive Sensing, the more the incoherence between sampled matrix and measurement matrix is, the better the full-band signal can be reconstructed. Therefore, the performance of signal fusion based on random sampling is better than that of fusion based on continuous sampled theoretically. In the current study, traditional multi-band signal fusion was extended to random sampled signal reconstruction, and Basic Pursuit was used for reconstructing full-frequency signal. Then, the sufficient condition of successful reconstruction with high probability was presented. The experimental results prove the advantage of this fusion method.