To improve the end precision of fiber Bragg grating ( FBG) flexible structure by using the orthogonal curvature 3D reconstruction method, a mapping relationship is established in the reconstructed curvature end coordinates and actual spatial coordinates through neural network. Firstly, the model of polyurethane glue rod is established by COMSOL simulation software. Two fiber Bragg grating strings are orthogonal arranged with 8 gratings, and a dynamic coordinate system is established by the recursive angle algorithm for three-dimensional reconstruction. The reconstructed end point coordinates are trained by back propagation (BP) neural network and extreme learning machine (ELM) neural network. The results show that the average training errors of BP neural network and ELM neural network are 0. 443 6 and 0. 008 2, respectively. Finally, an experimental platform is established to reconstruct the shape of the polyurethane glue stick under stress, and it is substituted into the ELM model for training. The correlation coefficient R 2 of the training results is 0. 985 8, and the root mean square error is 1. 363 0, which effectively improve the precision of the end coordinates of the shape reconstruction compared with the BP neural network.