Seasonal demand forecasting is critical for effective supply chain management. However, conventional forecasting methods face difficulties accurately estimating seasonal variations, owing to time-varying demand trends and limited data availability. In this paper, we propose a Fourier time-varying grey model (FTGM) to tackle this issue. The FTGM builds upon grey models, which are effective with limited data, and leverages Fourier functions to approximate time-varying parameters that allow it to represent seasonal variations. A data-driven selection algorithm adaptively determines the appropriate Fourier order of the FTGM without prior knowledge of data characteristics. Using the well-known M5 competition data, we compare our model with state-of-the-art forecasting methods taken from grey models, statistical methods, and architectures of neural network-based methods. The experimental results show that the FTGM outperforms popular seasonal forecasting methods in terms of standard accuracy metrics, providing a competitive alternative for seasonal demand forecasting in retail companies.