How can we learn the normal behavior of some communication processes and predict whether a single communication is under attack, with massive network traffic data representing the time costs of each stage in a single communication process? This paper introduces a statistical method for detecting network traffic anomalies using the Gaussian mixture model. There are two aspects to our contributions. First, we show how to learn the normal behavior of a communication process under the assumption that its time costs are generated from the Gaussian mixture model. Secondly, we show that with the learned Gaussian mixture model, we can predict whether a data point is under attack by computing the likelihood that the data point is drawn from the learned Gaussian distribution. The experimental results show that our method reached high accuracy in some cases, while in some other cases that are more complicated, the data point may have more factors and cannot be represented simply by only one Gaussian mixture model.