Cement grouting is widely used in rock tunnelling to control groundwater inflow by sealing rock fractures. Accurately predicting grout propagation in rock fractures is crucial for the design, execution, and monitoring of rock grouting in engineering applications. Current methods rely on theoretical models, such as the real-time grouting control (RTGC) method, which is derived based on simplified fracture geometries like smooth parallel plates/disks. However, real rock fractures consist of rough surfaces with variable apertures. In this study, we present a computational model for theoretically predicting the propagation of non-Newtonian cement grout in variable fracture apertures. This model is validated with laboratory test data on grout propagation in a one-dimensional varying aperture long slot (VALS). We also analysed the impact of varying aperture on cement grout propagation processes. Our findings demonstrate that the presented computational model predicts the grout propagation process in this geometry with good accuracy. Moreover, we observed that varying aperture significantly affects the grout propagation process in fractures. The insights provided by our model and analysis results are potentially useful in rock tunnelling projects, specifically for the theoretical analysis of cement grout propagation in rock fractures.