Deep　learning　has　achieved　a　preliminary　success　in　image　compression　due　to　the　ability　to　learn　the　nonlinear　spaces　with　compact　features　that　training　samples　belong　to.　Unfortunately,　it　is　not　straightforward　for　the　network　based　image　compression　methods　to　code　multiple　highly　related　images.　In　this　paper,　we　propose　a　co-prediction　based　image　compression　(CPIC)　which　uses　the　multi-stream　autoencoders　to　collaboratively　code　the　multiple　highly　correlated　images　by　enforcing　the　co-reference　constraint　on　the　multi-stream　features.　Patch　samples　fed　into　the　multi-stream　autoencoder,　are　generated　through　corresponding　patch　matching　under　permutation,　which　helps　the　autoencoder　to　learn　the　relationship　among　corresponding　patches　from　the　correlated　images.　Each　stream　network　consists　of　encoder,　decoder,　importance　map　network　and　binarizer.　In　order　to　guide　the　allocation　of　local　bit　rate　of　the　binary　features,　the　important　map　network　is　employed　to　guarantee　the　compactness　of　learned　features.　A　proxy　function　is　used　to　make　the　binary　operation　for　the　code　layer　of　the　autoencoder　differentiable.　Finally,　the　network　optimization　is　formulated　as　a　rate　distortion　optimization.　Experimental　results　prove　that　the　proposed　compression　method　outperforms　JPEG2000　up　to　1.5　dB　in　terms　of　PSNR.