The position and altitude of a sub-reflector have an important influence on the pointing accuracy of a radio telescope. With the increase of the antenna aperture, the stiffness of the support structure for the sub-reflector decreases. This causes deformation of the support structure when environmental loads, such as gravity, temperature, and wind load, are applied to the sub-reflector, which will seriously influence antenna pointing accuracy. This paper proposes an online measurement and calibration method for assessing the deformation of the sub-reflector support structure based on the Fiber Bragg Grating (FBG) sensors. Firstly, a reconstruction model between the strain measurements and the deformation displacements of a sub-reflector support structure is established based on the inverse finite element method (iFEM). In addition, a temperature-compensating device with an FBG sensor is designed to eliminate the effects of temperature variations on strain measurements. Considering the lack of the trained original correction, a non-uniform rational B spline (NURBS) curve is built to extend the sample data set. Next, a self-structuring fuzzy network (SSFN) is designed for calibrating the reconstruction model, which can further improve the displacement reconstruction accuracy of the support structure. Finally, a full-day experiment was carried out using a sub-reflector support model to verify the effectiveness of the proposed method.