A modified cellular automaton (MCA) model has been extended to the ternary alloy system by coupling thermodynamic and phase equilibrium calculation engine PanEngine. In the present model the dendrite growth is driven by the difference between the local equilibrium liquidus temperature and local actual temperature, incorporating the effect of curvature. The local equilibrium liquidus temperature is calculated with PanEngine according to the local liquid concentrations of two solutes, which are determined by numerically solving the species transport equation in the domain. Model validation was carried out through the comparison of the simulated values to the prediction of the Scheil model for solute profiles in the primary dendrites. The simulated data with zero solid diffusivity and limited liquid diffusivity were increasingly close to the Scheil profiles as the solidification rate decreased. The simulated microstructure and microsegregation in an Al-Cu-Mg ternary alloy were compared with those obtained experimentally.