A high-performance, low-cost demodulation system is essential for fiber-optic sensor-based measurement applications. This paper presents a demodulation system for FBG sensors based on a long-period fiber grating (LPG) driven by artificial intelligence techniques. The LPG is applied as an edge filter to convert the spectrum drift of the FBG sensor into transmitted intensity variation, which is subsequently fed to the proposed sensor demodulation network to provide high-precision wavelength interrogation. The sensor demodulation network consists of a generative adversarial network (GAN) for data augmentation and a dense neural network (DNN) for wavelength interrogation, the former addresses the drawback that traditional machine learning models rely on a large-scale dataset for satisfactory performance, while the latter is used to model the relationship between transmitted intensity and wavelength for demodulation. Experiments demonstrate that the proposed system has excellent performance and can achieve wavelength interrogation precision of ±3 pm. In addition, the effectiveness of the GAN is demonstrated. With a wide demodulation range, high performance, and low cost, the system can provide a new platform for fiber-optic sensor-based measurement applications.