The International Civil Aviation Organization (ICAO) has proposed satellite-based navigation to meet the upcoming flight demand. However, the aircraft positioning accuracy based on the Global Navigation Satellite System (GNSS) is of vital importance as it affects flight safety and efficiency. To assess the aircraft positioning accuracy, a Self-Evaluated Method (SEM) just using the Quick Access Recorder (QAR) data is proposed. It adopts the Euclidean distance between two adjacent moments of the aircraft by the Haversine formula, and then it is compared with the distance calculated by the ground speed and flight time. Among, the required data are all from the QAR dataset. The QAR data related to the flights departing from the Guangzhou International Airport in June 2019 are adopted, including A320, A321, B737, and B738. The average horizontal errors of the four types of aircraft at different latitudes and different flight phases were evaluated. The experimental results demonstrate that the average horizontal error of Airbus series aircraft (A320 and A321) is about 7 m, and the horizontal error of Boeing series aircraft (B737 and B738) is 12 m. We believe that the findings could provide a reference for Air Traffic Management (ATM) system.