Safety is a top priority for civil aviation. Data mining in digital Flight Data Recorder (FDR) or Quick Access Recorder (QAR) data, commonly referred as black box data on aircraft, has gained interest from researchers, airlines, and aviation regulation agencies for safety management. New anomaly detection methods based on supervised or unsupervised learning have been developed to monitor pilot operations and detect any risks from onboard digital flight data recorder data. However, all existing anomaly detection methods are offline learning - the models are trained once using historical data and used for all future predictions. In practice, new QAR data are generated by every flight and collected by airlines whenever a datalink is available. Offline methods cannot respond to new data in time. Though these offline models can be updated by being re-trained after adding new data to the original training set, it is time-consuming and computational costly to train a new model every time new data come in. To address this problem, we propose a novel incremental anomaly detection method to identify common patterns and detect outliers in flight operations from FDR data. The proposed method is based on Gaussian Mixture Model (GMM). An initial GMM cluster model is trained on historical offline data. Then, it continuously adapts to new incoming data points via an expectation-maximization (EM) algorithm. To track changes in flight operation patterns, only model parameters need to be saved, not the raw flight data. The proposed method was tested on two sets of simulation data. Comparable results were found from the proposed online method and a classic offline model. A real-world application of the proposed method is demonstrated using FDR data from daily operations of an airline. Results are presented and future challenges of using online learning scheme for flight data analytics are discussed.