In this work we present experimental and theoretical investigations of the directional solidification of Al-36 wt% Ni alloy. A phase-field approach (Folch and Plapp 2005 Phys. Rev. E 72 011602) is coupled with the CALPHAD (calculation of phase diagrams) method to be able to simulate directional solidification of Al-Ni alloy including the peritectic phase Al(3)Ni. The model approach is calibrated by systematic comparison to microstructures grown under controlled conditions in directional solidification experiments. To illustrate the efficiency of the model it is employed to investigate the effect of temperature gradient on the microstructure evolution of Al-36 wt% Ni during solidification.