Gravity waves can influence weather and climate patterns on various temporal and spatial scales in atmosphere. Despite their recognized importance, there are clearly a lack of sufficient and accurate observations from currently available satellite observing systems to satisfy the requirements of many satellite users. Common method to detect gravity waves is to measure bright temperature (BT) anomalies, which rely on an initial efficient background removal method. Before gravity waves can be extracted from Atmospheric Infrared Sounder (AIRS) raw radiances, Hoffmann and Alexander (2010) used a fourth-order polynomial fitting (4PF) method to remove the background variations. In this study, we propose a new strategy, an optimal orthogonal polynomial fitting (OPF) method using Chebyshev Polynomials as basis functions, to remove the background variations and estimate BT perturbations. By extending the classic 4PF method to the fifth-order polynomial fitting (5PF) method, and combining the Cressman interpolation (CI) method, some experiments are designed to validate the feasibility and superiority of OPF method. The results show that OPF is the optimal method to remove the limb-brightening effect in the extraction of gravity wave signals generated by typhoons. In addition, what we noticed is that an appropriate fitting orders have to be selected to get more accurate BT anomalies signals in the experiments to extract gravity wave signals.