Real-time and precise prediction for traffic of networks is critically important for allocating the optimal computing/network resources based on users' business requirements, analyzing the network performance, and realizing intelligent congestion control and high-accuracy anomaly detection. The dramatic growth of users' applications significantly increases the volume, uncertainty, and complexity of workload, thereby making it highly challenging to precisely predict future net-work traffic. Temporal Convolutional Networks (TCNs) and Long Short-Term Memory (LSTM) can be effectively used to analyze and predict time series. This work designs an improved prediction approach for the prediction of network traffic, which combines a Savitzky-Golay filter, TCN, and LSTM, called ST-LSTM for short. It first removes the noise of data with the filter of Savitzky-Golay. It then investigates temporal characteristics of data by using TCN. At last, it investigates the long-term dependency in the time series by using LSTM. Experimental results on a real-life website dataset show the prediction accuracy of ST-LSTM is higher than autoregressive integrated moving average, support vector regression, eXtreme Gradient Boosting, backpropagation, TCN, and LSTM, in terms of several commonly used performance indicators.