Abstract: The safety risk of top fractured coal and rock mass is caused by large-scale and high-intensity mining and deep mining. Drilling grouting is one of the main methods used to seal fractures and strengthen coal and rock mass. Due to the relatively less research on the theory of high-position grouting for fractures, the design of high-position grouting lacks sufficient theoretical basis. In order to explore the diffusion law of high-position grouting slurry in coal and rock fractures, the smooth plate fractures with arbitrarily inclined finite boundaries and Bingham fluids were taken as the research objects, and the mathematical model of high-position grouting diffusion in fractures was established. The ANSYS FLUENT numerical software was used to numerically solve the mathematical model. The diffusion front, flow distribution and pressure field variation of slurry in the process of fracture flow under different fracture inclination angles and grouting rates were studied. Based on this, the mathematical model of slurry high-position flow was established, and the analytical solution under the condition of constant grouting rate was derived. The research shows that based on the evolution law of the diffusion front, the flow process can be divided into three stages: the free diffusion stage, the transition stage and the restricted accumulation stage. The influence of the fracture dip angle on the high-position diffusion distance gradually decreases with the evolution of the flow stage, and the influence of the grouting flow rate on the high-position diffusion distance gradually increases with the evolution of the flow stage. Excessive fracture inclination increases the loss of high-position flow and accelerates the transition of flow stage, while excessive grouting rate slows down the loss of high-position flow and accelerates the transition of flow stage. The increase of grouting rate and fracture inclination will lead to the increase of grouting pressure, and the grouting pressure changes abruptly after the slurry enters the restricted accumulation stage. The high-position flow can be divided into the diffusion stage and the accumulation stage based on the critical state of the equivalent circle radius of the high-position flow diffusion form. The equivalent central angle obtained by inversion in different stages has an excellent correlation with the grouting rate, crack inclination angle and grouting time. After comparing with the calculation results of the numerical model, it is concluded that the samples with a relative error of less than 20% in the mathematical model of slurry high-position flow accounts for 97%, and the samples with a relative error of less than 10% accounts for 78.4%. The mathematical model of slurry high-position flow has been proved to have certain rationality. The scope of the slurry spreading to the deep part of high-position fractures in different time periods is affected by the fracture boundary. Only when the bottom fracture space is filled will the slurry accumulate to the deep part under the support of the fracture boundary. Therefore, when designing high-position grouting on site, the boundary extent of the fractured area should be identified. A lower grouting rate can be used to extend the duration of the free diffusion stage when plugging the cracks in the surface area of the overlying coal and rock to achieve rapid sealing of the bottom crack space. When grouting and filling the deep area of coal-rock fracture, a higher grouting rate can be used first. When the pressure gauge changes abruptly, it indicates that the grout has entered the limited accumulation stage. At this time, the grouting rate can be reduced to control the grouting pressure within a safe and controllable range.