Vacancy plays important roles during the precipitation of age hardening precipitates in aluminium alloys. In this work a numerical model is developed to simulate the evolution of non-equilibrium excess vacancies in multicomponent aluminium alloys. In the present model, the finite volume scheme is applied to derive the spatial distribution of vacancy site fraction across grains by solving the diffusion equations of vacancies under the influence of solute elements. The annihilation of excess vacancies on dislocation jogs and grain boundaries has been carefully considered. Binding energies between the solute atoms and vacancies predicted by first-principles calculations are used to handle the trapping of excess vacancies to solute atoms and clusters. With the model, the global evolution of vacancies as functions of cooling rate from solution treatment, ageing temperature and ageing time has been achieved. The model has been validated with a couple of experimental alloys, and the simulation results have been compared with previous analytical models and numerical models. It shows that the present model can be well applied to get a deeper understanding of the precipitation kinetics of age hardening aluminium alloys under the influence of excess vacancies, which is important for further optimising thermomechanical processing parameters to improve the macroscopic mechanical properties and corrosion properties of the materials.