Cladding waveguide fiber Bragg gratings (FBGs) provide a compact and simple solution for fiber shape sensing. The shape sensing accuracy is limited by birefringence, which is induced by bending and the non-isotropic FBG structure (written by femtosecond laser point-by-point technique). An algorithm based on an artificial neural network for fiber shape sensing is demonstrated, which enables increased accuracy, better robustness, and less time latency. This algorithm shows great potential in the application of high-accuracy real-time fiber shape measurements.