The precipitation kinetics of ordered gamma' (L1(2)-Ni3Al) phase from nucleation and growth to coarsening in a Ni-Al alloy is studied by phase field simulation. The initial nucleation of the gamma' phase is quantitatively described by the variations of composition and order parameter profiles of the initial Al-enriched cluster, and the coarsening kinetics is clarified with the time exponent of the average particle radius of gamma' phase. The precipitation of the gamma' phase from the supersaturated gamma solid solution goes through the non-stoichiometric ordered phase, stoichiometric ordered phase, growth and coarsening. The time exponent of the average radius of the gamma' phase with coherent equilibrium is smaller than that indicated by the Lifshitz-Slyozov-Wagner theory at the coarsening stage, and it decreases from 1.35 of the nucleation and growth stage to 0.22 of the coarsening stage. The peak of the particle size distribution decreases and the width of the particle size distribution increases as the aging progresses. As the average radius of the gamma' phase increases, the average aspect ratio of the gamma' phase undergoes a slowly increase to a fast increase from nucleation to growth stage, then goes into a relatively stable state at the coarsening stage. (C) 2016 Elsevier B.V. All rights reserved.