[Purposes] To improve traffic service quality under various events, it is vital to efficiently detect network outlier traffic flow. [Methods] Considering the periodic characteristics of typical traffic flow under normal conditions (short for "normal traffic flow"), we first define the observed traffic flow during various events as the sum of normal traffic flow and abnormal traffic flow caused by the events. It allows us to model the network outlier traffic flow detection problem as a matrix decomposition problem. Next, by leveraging the low-rank property of the normal traffic flow matrix and the sparsity property of the outlier traffic flow matrix, the matrix decomposition problem is further converted into a convex optimization problem. An accelerated proximal gradient solution algorithm is proposed accordingly. Finally, we consider the scenario elements including detection scale, event frequency, and the magnitude of random traffic flow fluctuations, and the model is validated using both simulated data and real-world metro passenger flow data from a city in Southern China. [Findings] The results demonstrate that the accuracy of outlier traffic flow detection is negatively correlated with the magnitude of random fluctuations of traffic flow under normal conditions. In various simulation scenarios, the detection accuracy of the proposed model achieves over 73.67%, which is significantly higher than traditional models. In the real-world metro passenger flow scenario, the target model effectively reduces the interference of random passenger flow, and the detection accuracies for entry and exit flow are 77.42% and 78.07%, respectively, also achieving the highest accuracy. [Conclusions] The proposed model not only exhibits strong robustness in outlier traffic flow detection, but the output also reflects the traffic flow change caused by the events, and provides data support for emergency resource allocation.