This paper proposes a compression-combined digital image encryption method which is robust against consecutive packet loss and malicious shear attack. We utilize the characteristics of compressive sensing, dimensional reduction and random projection, to compress and encrypt a digital image simultaneously. On this basis, block Arnold scrambling is used to permutate the position of measurements. Bit wise XOR operation is executed on the quantized binary bit stream to dissipate the Gaussian distribution property of cipher image. In this paper, one dimensional Logistic mapping is used to generate chaotic sequences, which will be regarded as the parameters of block Arnold transformation and the pseudo-random sequence for XOR operation. Numerical experiments show that the cipher image has following features, robustness, low data volume, incoherence, key sensitivity, and resistance to brute force attack.