Precise　real-time　prediction　of　the　number　of　future　network　attacks　cannot　only　prompt　cloud　infrastructures　to　fast　respond　to　them　and　protect　network　security,　but　also　prevents　economic　and　business　losses.　In　recent　years,　neural　networks,　e.g.,　Bi-direction　Long　and　Short　Term　Memory　(LSTM)　and　Temporal　Convolutional　Network　(TCN),　have　been　proven　to　be　suitable　for　predicting　time　series　data.　Attention　mechanisms　are　also　widely　used　for　the　time　series　prediction.　In　this　work,　we　propose　a　novel　hybrid　deep　learning　prediction　method　by　combining　the　capabilities　of　a　Savitzky-Golay　(SG)　filter,　TCN,　Multi-head　self　attention,　and　BiLSTM　for　the　prediction　of　network　attacks.　This　work　first　adopts　a　SG　filter　to　eliminate　noise　in　the　raw　data.　It　applies　TCN　to　extract　short-term　features　from　the　sequences.　It　then　adopts　multi-head　self　attention　to　capture　intrinsic　connections　among　features.　Finally,　this　work　adopts　Bi-LSTM　to　extract　bi-directional　and　long-term　correlations　in　the　sequences.　Experimental　results　with　a　real-life　dataset　show　that　the　proposed　method　outperforms　several　typical　algorithms　in　terms　of　prediction　accuracy.　　©　2022　IEEE.