Abstract: Permeability is the core transport parameter of heat pipe wicks, and its accurate prediction is essential for the design of high-temperature heat pipes used in advanced heat pipe cooled reactors. Sintered-arterial composite wicks balance high capillary force and high permeability, but their cross-scale microstructure makes traditional computational fluid dynamics methods difficult to perform fine simulations. The lattice Boltzmann method (LBM) has unique advantages in this field. It can accurately handle complex porous media geometries, has natural parallelism suitable for large-scale computing, and provides clear physical images. This study aims to systematically investigate the permeability characteristics of a sintered-arterial composite wick and establish a predictive model, thereby providing crucial insights for the design of high-performance wicks. In this paper, a GPU-accelerated LBM solver based on the D3Q19 discrete velocity model and half-step bounce-back boundary condition was developed. Large-scale simulations of liquid sodium flow at 850 °C were performed, achieving a maximum grid scale of over 100 million on a single NVIDIA RTX A6000 graphics card. The sintered porous matrix was reconstructed using the quartet structure generation set (QSGS) method. Firstly, a comprehensive parametric study on the pure sintered wick was conducted to analyze the effects of porosity (ε), initial seed distribution (S_\mathrmd), and reference growth probability (G_\mathrmref). Subsequently, circular channel of varying diameters (D) were introduced into the sintered matrix to form the composite wick. The flow dynamics were analyzed through velocity contours and streamlines. Finally, a simplified permeability prediction model for the composite wick was developed based on the superposition of independent Poiseuille flow in the arterial and Darcy flow in the sintered matrix. For the pure sintered wick, permeability increases significantly with ε but decreases with a higher S_\mathrmd, while remaining largely insensitive to G_\mathrmref. In the composite wick, the overall permeability increases with the channel diameter, transitioning through three distinct regimes: sintered-matrix-dominated, mixed-flow, and arterial-dominated flow. The flow in the arterial exhibits a parabolic profile, similar to laminar pipe flow, while fluid exchange occurs at the arterial-matrix interface. The proposed prediction model agrees well with the LBM simulation results, with a maximum relative deviation of 11.4%. However, the model systematically underestimates the permeability because it neglects the interfacial fluid exchange, which is quantified by the positive difference between the equivalent arterial diameter and the actual diameter. The magnitude of this deviation increases with ε but decreases with S_\mathrmd, showing negligible dependence on G_\mathrmref. This work demonstrates the superior performance of LBM in cross-scale porous media flow simulation, clarifies the key factors governing composite wick permeability, and provides a practical predictive tool for the optimized design of high-performance wicks in heat pipe cooled reactors