In　the　procedures　of　image　acquisition,　compression,　and　transmission,　captured　images　usually　suffer　from　various　degradations,　such　as　low-resolution　and　compression　distortion.　Although　there　have　been　a　lot　of　research　done　on　image　restoration,　they　usually　aim　to　deal　with　a　single　degraded　factor,　ignoring　the　correlation　of　different　degradations.　To　establish　a　restoration　framework　for　multiple　degradations,　a　joint　deep-network-based　image　restoration　algorithm　is　proposed　in　this　paper.　The　proposed　convolutional　neural　network　is　composed　of　two　stages.　Firstly,　a　de-blocking　subnet　is　constructed,　using　two　cascaded　neural　network.　Then,　super-resolution　is　carried　out　by　a　20-layer　very　deep　network　with　skipping　links.　Cascading　these　two　stages　forms　a　novel　deep　network.　Experimental　results　on　the　Set5,　Set14　and　BSD100　benchmarks　demonstrate　that　the　proposed　method　can　achieve　better　results,　in　terms　of　both　the　subjective　and　objective　performances.