In this paper, a CALPHAD (CALculation of PHAse Diagram)-based viscosity model has been established for multicomponent liquid systems, using Al-Ni-Fe-Co melt as an example. Firstly, the viscosity databases of pure Fe and Co liquids were assessed following an Arrhenius equation based on the available experimental viscosity data. The viscosity databases of pure Ni and Al liquids were adopted from our previous research and literature. Subsequently, viscosity databases of the Al-Fe, Al-Co, Fe-Co, Fe-Ni, Co-Ni binary liquids were assessed using the CALPHAD model and compared with the available experimental viscosity data. For the first time, the temperature- and composition-dependent binary interaction parameters were used to describe the non-linear viscous behavior due to the chemical short-range order. The viscosities of ternary Al-Fe-Ni liquid were predicted from the databases directly extrapolated from sub-binary systems using the Redlish-Kister-Muggianu model. The good agreement of viscosity between present calculations and available experiments in Al alloy melts demonstrated that the CALPHAD-based viscosity model is suitable for predicting the viscosity of multicomponent liquids as well as their complex temperature-composition-phase-viscosity relationships.