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Traditional information hiding algorithms cannot maintain a good balance of capacity, invisibility and robustness. In this paper, a novel blind colour image information hiding algorithm based on grey prediction and grey relational analysis in the Discrete Cosine Transform (DCT) domain is proposed. First, this algorithm compresses the secret image losslessly based on the improved grey prediction GM(1,1) (IGM) model. It then chooses the blocks of rich texture in the cover image as the embedding regions using Double-dimension Grey Relational Analysis (DGRA). Finally, it adaptively embeds the compressed secret bits stream into the DCT domain mid-frequency coefficients, which are decided by those blocks' Double-Dimension Grey Correlation Degree (DGCD) and Human Visual System (HVS). This method can ensure an adequate balance between invisibility, capacity and robustness. Experimental results show that the proposed algorithm is robust against JPEG compression (46.724 6 dB when the compression quality factor is 90%), Gaussian noise (45.531 3 dB when the parameter is (0,0.000 5)) etc., and it is a blind information hiding algorithm that can be extracted without an original carrier.