Abstract: The lowest compressive sampling rate for non-uniform block sparse signals and the decay property of restricted isometry constant of measure matrix is theoretically analyzed. A blind recovery algorithm without knowing the order and distribution of blocks is proposed. The algorithm improves the estimation precision of nonzero values positions by dividing the block sparse signal uniformly for several times according to successive decreasing block length, and then eliminating the zero value positions in the uniform blocks using Orthogonal Matching Pursuit (OMP) method, which leads to a better recovery result. The performance of the blind recovery algorithm is analyzed and simulation results verify the effectiveness and practicality further.