Traditional Block compressed sensing (BCS) schemes encode nature images via a fixed sampling rate without taking the sparsity level diffierences among the blocks into consideration. In order to improve the sampling efficiency, a permutation-based BCS scheme with separate reconstruction is considered in this paper. The error performance bound of BCS scheme is carefully analyzed, and it is revealed that the smaller the maximum block sparsity level of the 2D signal is, the better reconstruction performance the algorithm has. According to the theoretical analysis result, an interweaving-permutationbased BCS strategy is investigated. In the proposed approach, the maximum block sparsity level of the 2D signal can be reduced significantly by interweaving permutation. As a result, better reconstruction performance can be achieved. Simulation results show that the proposed approach improves the Peak signal-to-noise ratio (PSNR) of reconstructed-images significantly.