Understanding and predicting the morphology, kinetics and hardening effects of precipitates are critical in improving the mechanical properties of Al-Cu-based alloys through controlling the temperature and duration of the heat treatment process. In this work, we present a comprehensive phase-field framework for simulating the kinetics of θ′ precipitates in W319 alloys, integrating the thermodynamic and diffusion mobility databases of the system, the key precipitate anisotropic energy contributions from literature and first-principles calculations, as well as a nucleation model based on the classical nucleation theory. By systematically performing phase-field simulations, assuming the precipitate peak number densities determined from experiments, we optimize the model parameters to obtain the best possible match to the average diameters, thicknesses and volume fractions of precipitates from experimental measurements at 190, 230 and 260 °C. With these parameters available, the phase-field simulations can be performed at other aging temperatures. The possible extensions of the current phase-field model for more accurate prediction of the precipitate behaviors in W319 alloys will also be discussed.