We conducted ab initio molecular dynamics simulations to investigate the dynamic properties of the liquid Ti–Al–Ni ternary alloy system at 2033 K. Through simulations across the entire composition range, we revealed the complex compositional dependence of self-diffusion coefficients and viscosity. The self-diffusion coefficients of Ti, Al, and Ni exhibit nonlinear distribution characteristics, while viscosity shows non-monotonic compositional dependence, with lower viscosity in Al-rich regions and higher viscosity in Ni-rich regions. To understand the structural origins of these behaviors, we analyzed chemical short-range order and local fivefold symmetry structures using Warren-Cowley parameters and fivefold symmetry parameters, uncovering a close correlation between atomic-scale structural features and dynamic properties. Evaluation of the Stokes-Einstein relation revealed varying degrees of deviation from its predicted viscosity values across composition regions. We observed a negative correlation between free volume fraction and viscosity, with varying strengths in different regions. These findings provide new perspectives for understanding the complex dynamic properties of Ti–Al–Ni liquid alloys.