Abstract: Grouting reinforcement is the main means to seal cracks and repair rock mass. It is very important for the design and practice of grouting parameters to clarify the grouting diffusion law of inclined cracks in horizontal grouting holes of surrounding rock of roadway side. This study focuses on Bingham fluid flow within arbitrarily inclined, finite-boundary smooth parallel-plate fractures. A theoretical model for grouting diffusion in inclined fractures was established, incorporating the time-dependent viscosity of Bingham fluid and the grout diffusion radiation angle. The liquid-gas two-phase interface control equations and Navier-Stokes equations were solved using the finite element method, with the volume fraction method employed to quantitatively characterize grout diffusion patterns and distances, validating theoretical results through comparative analysis. Furthermore, the influence of grouting pressure differentials, fracture apertures, and fracture inclination angles on diffusion morphology and distance was systematically investigated. The results show that the theoretical model is basically consistent with the grouting diffusion law of inclined fracture obtained by numerical simulation. The maximum error of diffusion distance in the fracture area above and below the grouting hole is 5.6 % and 6.1 % respectively, which verifies the feasibility of the theoretical model. When the slurry diffusion radiation angle is 0° and 180°, the diffusion distance reaches the maximum and minimum respectively, and the larger the fracture opening is, the more significant the difference is. When the dip angle of the fracture is 0°, the slurry in the fracture area shows a central symmetrical circular shape along the grouting hole. With the increase of the dip angle of the fracture, the diffusion form of the slurry evolves into an elliptical shape symmetrically along the grouting hole. The trace line in the middle of the fracture area above is accompanied by depression characteristics, and the range and maximum diffusion distance of the fracture trace line above are smaller than those of the fracture below. With the increase of grouting time, the micro-depression characteristics gradually weaken, and the ellipse-like shape continues to expand. The increase of the range and the maximum diffusion distance of the slurry diffusion trace line in the fracture area above are smaller than those of the fracture below.