The prediction and accurate warning of CDN bandwidth outliers have always been the focus and difficulty of network operation. For this reason, the study proposes and implements a new algorithm framework, the serial LSTM (long short-term memory) network with locally weighted regression, based on the LSTM network with time series. The framework uses the time-series interpolation sampling method to construct the data set, and the local weighting algorithm is integrated into the fitting model based on least square regression for initial prediction. The prediction result is serialized with the LSTM time series model for the final bandwidth outlier prediction. The 4sigma method is used to determine whether the bandwidth is abnormal at a certain moment, and an abnormal alarm is issued according to the grade standard. The experimental results show that the model is effective for the prediction and alarm of bandwidth outliers.