Well-trained　neural　network　models　are　deployed　on　edge　servers　to　provide　valuable　inference　services　for　clients.　To　protect　data　privacy,　a　promising　way　is　to　exploit　various　types　of　secret　sharing　to　implement　privacy-preserving　neural　network　inference.　However,　existing　schemes　suffer　high　communication　rounds　and　overhead,　making　them　hardly　practical.　In　this　paper,　we　propose　Cenia,　a　new　communication-efficient　privacy-preserving　neural　network　inference　model.　Specifically,　we　exploit　arithmetic　secret　sharing　to　develop　low-interaction　secure　comparison　protocols,　that　can　be　used　to　realize　secure　activation　layers　(e.g.,　ReLU)　and　secure　pooling　layers　(e.g.,　max　pooling)　without　expensive　garbled　circuit　and　oblivious　transfer　primitives.　Besides,　we　also　design　secure　exponent　and　division　protocols　to　realize　secure　normalization　layers　(e.g.,　Sigmoid).　Theoretical　analysis　demonstrates　the　security　and　low　complexity　of　Cenia.　Extensive　experiments　have　also　been　conducted　on　benchmark　datasets　and　classical　models,　and　experimental　results　show　that　Cenia　achieves　privacy-preserving,　accurate,　and　efficient　neural　network　inference.　Particularly,　Cenia　can　achieve　37.5%　and　60.76%　of　Sonic＇s　communication　rounds　and　overhead,　respectively,　compared　to　Sonic　(i.e.,　the　state-of-the-art　scheme).