Ensuring the long-term durability of glass fiber-reinforced polymer (GFRP) bars poses a significant challenge in practical applications, particularly in marine environments. Moisture absorption by GFRP bars causes hydrolysis and plasticization of the polymer matrix, resulting in a decline in both their stiffness and strength. Furthermore, the penetration of detrimental ions (e.g., OH-) with moisture accelerates the degradation of GFRP bars. Therefore, clarifying the moisture absorption behavior of GFRP bars is crucial for investigating their durability. Previous studies have indicated that the initial moisture absorption in GFRP bars conforms to the Fickian model. However, with prolonged exposure, anomalous diffusion behavior emerges, characterized as non-Fickian diffusion. This paper reviews existing models for non-Fickian diffusion, highlighting their shortcomings. Gravimetric experiments were then conducted on GFRP bars with diameters of 6, 10, and 14 mm, immersed in portable water at temperatures approximately 23, 40, and 60 °C. Based on the test results and underlying mechanisms, an improved model, named the Weibull relaxation (WR) model, was proposed and validated using the particle swarm optimization (PSO) algorithm for regression analysis. The new model not only exhibits better agreement with the test results but also incorporates fitting parameters with clear physical interpretations. Its distinct advantage over existing models is that it is able to more realistically capture the mechanisms governing the moisture absorption of GFRP bars.