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.