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This paper proposes a secure image block compressive sensing scheme based on a key-controlled sparse basis matrix and key-controlled measurement matrix. In the proposed scheme, the original image is first divided into blocks, then inter-block scrambling is employed using the Arnold transform. Second, the resulting scrambled blocks are secure CS, which consists of a chaotic discrete cosine transform, sparse basis matrix, and a chaotic discrete Hartley transform measurement matrix, based on row scrambling with a chaotic sequence. The measured data obtained using CS is encrypted using bitwise XOR and pixel scrambling operations based on chaotic maps. The simulation results show that the application of a suitable sub block size for the proposed scheme can achieve good image reconstruction performance in terms of peak-signal to noise ratio merits when compared to the conventional chaotic measurement matrix and random measurement matrix schemes. Our proposed block secure CS can maintain the security of image data, and reduce the CS run time.