In a serial wavelength division multiplexing (WDM) fiber Bragg grating (FBG) sensor network, it is well known that there are challenges in separating overlapping signals, which require high precision and low delays. And using an optical spectrum analyzer as a data source result in demodulation models that are impractical for use in engineering applications. Therefore, an overlapping spectral demodulation model based on transfer learning using a charge-coupled device (CCD) interrogator and light gated recurrent unit (Li-GRU) neural networks is proposed. This model can achieve a low signal demodulation error, even when applied to data collected using a CCD interrogator with low spectral resolution and a high signal-to-noise ratio. We describe the operation principle of the Li-GRU neural network and discuss the impact of transfer learning and CNN feature extraction layers on demodulation performance. The experimental results show that lowest root mean square error of our proposed model is 1.93 pm, and the single inference time of the model on the CPU is <45 ms. This serial WDM fiber grating demodulation method can be effectively applied in temperature and strain measurement demodulation.