Cement grouting has been widely used in rock tunneling to reduce groundwater inflow by sealing rock fractures. However, the injected cement grout often encounters hydraulic erosion that affects the safety and sustainability of rock tunnels in the long term. Analysis of the long-term hydraulic erosion effect on cement grout in rock fractures is therefore important for the safety and sustainability development of rock tunnel engineering. In this work, a hydraulic erosion model for analyzing cement grout erosion in a homogeneous fracture is established and used to theoretically investigate the transmissivity evolution of the grouted fracture under longterm hydraulic erosion. In the present model, the fracture seepage characteristics, solid erosion theory and mass conversation for water-solid two-phase flow are considered, and the mathematical model as a set of partial differential equations is established. Based on laboratory tests, the key parameters (e.g., erosion coefficient) are calibrated and the erosion model is validated. Numerical simulations are conducted by numerically resolving the mathematical model. The results show that the erosion phenomenon first occurs in the edge areas of the grouted area near the fracture boundary; the erosion area gradually expands toward the center of the grouted area. The porosity and flow velocity significantly increase in the area with relatively strong erosion effects. During the erosion process, the concentration of cement grout gradually increases along the seepage path until a more uniform distribution of cement particle concentration is achieved. Due to the erosion process, the spatial distribution of hydraulic pressure along the fracture direction transforms from a linear distribution to a nonlinear distribution. The effective fracture transmissivity increases nonlinearly along the erosion process. The presented erosion model and analysis results are potentially useful for the safety and durability assessment of rock tunnels.