Quantitative modelling of precipitation kinetics can play an important role in a computational materials design framework. For many material systems, e.g., the Fe-Cu system, the precipitates (rich in Cu at equilibrium) nucleate at a composition far away from the equilibrium. This in turn affects the precipitation kinetics, and the capability to model the compositional evolution of the Cu precipitates is therefore important. In the present work we propose a new approach implemented in a Langer-Schwartz-Kampmann-Wagner precipitation modelling framework where the concentration profile inside the precipitates is defined with an explicit function and the diffusive fluxes in both precipitates and matrix are solved concurrently to compute the growth rate of the precipitates. The new model is evaluated with respect to results from atom probe tomography for Cu precipitation in a 15–5 PH stainless steel. A parameter study of the effect of diffusion coefficients and interfacial energies is conducted, and it is concluded that the new model is capable of describing the experimentally determined evolution of the Cu precipitate volume fraction, mean radius, number density and composition.