An embedded atom method potential for Ni-Al alloys is developed. The expression of the embedded function is constructed by analogy with the density function theory. Both the repulsive function and the electron density function here have simple forms. The potential parameters of pure Al and Ni are fitted to the experimental values, including their lattice parameters, cohesive energies, vacancy formation energies and three elastic constants $(c_{11}, c_{12}, c_{13})$. The potential for the Ni-Al alloy are then constructed from the Ni and Al potentials. The equation of states and the phonon dispersion calculated by the present potential parameters are in good agreements with first-principles calculations and experimental data, indicating the reliability of the present potential.