Reducing data volume and improving signal-to-noise ratio (SNR) is of great importance for echoes from submerged targets, affected by serious marine environment noise. The echo from a target is made of its response to the incident wave with the superposition of highlights (sub-echoes from main constituents of the target). Each of these highlights can be seen as a block, and the echo therefore has a block-sparse feature. This paper proposes a compressive sensing method to leverage prior information (CSPI), in which knowledge of the incident wave and the block-sparse feature are leveraged into the dictionary structure and signal reconstruction. CSPI is illustrated with simulations and field measurements of backscattering for a 1:20 model of the Benchmark Target Strength Simulation Submarine. For simulated signals with different noise levels, CSPI can reconstruct an almost invisible signal (original SNR = 0 dB), and improve SNR by up to 13 dB (for an original SNR of 4 dB) down to a still significant SNR of 7 dB (for an original SNR of 0 dB). For field measurements, CSPI can obtain the same SNR as the original signal using only 13% of the data, increasing the SNR to 15 dB using 30% data, and increasing with the compression ratio.