The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study. The fracture is created from a measured surface of a granite rock sample. The Bandis model is used to calculate the fracture closure due to normal stress, and the fluid flow is simulated by solving the Reynold equation. The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture. The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures. It causes fracture closure and creates asperity contact areas, which significantly reduces the effective hydraulic aperture and enhances flow channeling. Consequently, the reduced aperture and enhanced channeling affect travel time distributions. In particular, the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport. The fracture normal stiffness correlates linearly with the 5th and 95th percentiles of the normalized travel time. The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.