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The evaluation of the thermodynamic data and the simulation of a four-phase peritectic-like reaction in Al-Cu-Ni alloys by means of the phase-field modeling is presented. A peritectic-like reaction in a ternary system is an univariant reaction, which means, the equilibrium compositions of all phases vary with the temperature. Using the Gibbs free energies of the phases we evaluated the equilibrium compositions and also the thermodynamic factors of phases which define the driving force of the transformation. In our modeling we apply the multi-phase field model which uses the mean concentrations as variables in the diffusion equation.In the four-phase reaction the product phase β can precipitate along with another product phase g on the primary phase, or β may be a potent nucleant for g too. The precise value of the nucleation rate used in the simulation was defined by comparison of the simulated microstructure to the experimental data.