Al-Ni-Y alloys show excellent glass forming ability and are very promising for structural materials. In order to study the phase equilibria of this ternary system the CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) approach is combined with results from first-principles calculations coupled with experimental data and existing CALPHAD models for the constituent binaries. The finite temperature thermodynamic properties including both enthalpy and entropy of ten ternary compounds in this system have been obtained through harmonic and quasi-harmonic approximations. The calculated formation enthalpy and lattice parameters showed good agreement with experiments. From the constructed thermodynamic database, phase equilibria and the liquidus projections were calculated. The solidification sequences for several alloys in this system were also studied through Scheil simulations and were compared with available experimental information.