Abstract: Accurate prediction of fiber-asphalt bond-slip behavior is crucial for evaluating asphalt concrete performance. Although the generalized grey Verhulst model (GGVM) handles saturated growth sequences well, it exhibits limitations in modeling highly nonlinear interfacial curves due to insufficient "new information priority" in its accumulation operator and crude background value construction that causeserror accumulation. To address these issues, this paper proposes a hybrid improved grey generalized Verhulst model (Mar-NIP�FO_GGVM). First, the new information priority fractional-order (NIP-FO) accumulation operator and background value adjustment coefficient are introduced to structurally enhance the model's capability to capture recent information and nonlinear dynamics. Subsequently, particle swarm optimization is employed for global parameter optimization, while the Markov chain is utilized for stochastic correction of prediction residuals. Finally, the model is applied to predict interfacial bond-slip curves of basalt, glass, and polyester fibers. Comparisons with the Popovics model and three other grey models validate the proposed model's effectiveness, applicability, and robustness. Results show that Mar-NIP-FO_GGVM outperforms all benchmarks across three scenarios, with simulation and prediction MAPEs below 7%, while accurately capturing different fibers' stage-wise characteristics. Statistical tests further confirm its significant advantages, establishing a high-precision, data-driven tool for fiber-asphalt micromechanical analysis.