Although　the　deep　learning　technology　has　shown　great　power　in　solving　the　complex　tasks,　these　neural　network　models　are　large　and　redundant　as　a　matter　of　fact,　which　makes　these　networks　difficult　to　be　placed　in　embedded　devices　with　limited　memory　and　computing　resources.　In　order　to　compress　the　neural　network　to　a　slimmer　and　smaller　one,　the　multi-grained　network　pruning　framework　is　proposed　in　this　paper.　In　our　framework,　the　pruning　process　was　divided　into　the　filter-level　pruning　and　the　weight-level　pruning.　In　the　process　of　the　filter-level　pruning,　the　importance　of　the　filter　was　measured　by　the　entropy　of　the　activation　tensor　of　the　filter.　In　the　other　process,　the　dynamic　recoverable　pruning　method　was　adopted　to　prune　the　weights　deeply.　Different　from　these　popular　pruning　methods,　the　weight-level　pruning　is　also　taken　into　account　based　on　the　employment　of　the　filter-level　pruning　to　achieve　more　effectively　pruning.　The　proposed　approach　is　validated　on　two　representative　CNN　models　-　AlexNet　and　VGG16,　pre-trained　on　ILSVRC12.　Experimental　results　show　that　AlexNet　and　VGG16　network　models　are　compressed　19.75×　and　22.53×　respectively　by　this　approach,　which　are　2.05　and　5.89　higher　than　the　classical　approaches　of　dynamic　Network　Surgery　and　ThiNet.　©　Springer　Nature　Singapore　Pte　Ltd.　2019.