Precise　and　real-time　prediction　of　future　network　attacks　can　not　only　prompt　cloud　infrastructures　to　fast　respond　and　protect　network　security　but　also　prevents　economic　and　business　losses.　In　recent　years,　neural　networks,　e.g.,　bidirectional　gated　recurrent　unit　(Bi-GRU)　network　and　temporal　convolutional　network　(TCN),　have　been　proven　to　be　suitable　for　predicting　time-series　data.　Attention　mechanisms　are　also　widely　used　for　the　prediction　of　the　time　series　of　network　attacks.　This　work　proposes　a　hybrid　deep　learning　prediction　method　that　combines　the　capabilities　of　Savitzky-Golay　(SG)　filter,　TCN,　multihead　self-attention,　and　Bi-GRU　(STMB)　for　the　prediction　of　network　attacks.　This　work　first　adopts　an　SG　filter　to　smooth　possible　outliers　and　noise　in　network　attack　traffic　data.　It　applies　TCN　to　extract　abstract　features　from　1-D　time　series　to　make　full　use　of　data.　It　then　adopts　multihead　self-attention　to　capture　internal　correlations　among　multidimensional　features,　by　increasing　the　weights　of　key　features　and　reducing　those　weight　of　non-key　features,　making　that　STMB　captures　important　features　adaptively.　Finally,　this　work　adopts　Bi-GRU　to　extract　bidirectional　and　long-term　correlations　in　the　time　series　to　improve　the　prediction　accuracy.　This　work　also　utilizes　a　hybrid　algorithm　named　genetic　simulated-annealing-based　particle　swarm　optimizer　to　determine　the　hyperparameter　setting　of　STMB.　Experimental　results　with　real-life　data　sets　show　that　STMB　outperforms　several　commonly　used　algorithms　in　terms　of　prediction　accuracy.