A comprehensive particle size distribution model has been developed for the simulation of γ′ precipitation in multicomponent Ni alloys. Nucleation, growth and coarsening of the precipitates are described by a particle size distribution. The growth rate of each precipitate class is calculated with a multi-component diffusion model formulated for non-diagonal matrices of diffusion coefficients. The model is fully coupled with CALPHAD calculations of the thermodynamic equilibrium at the interface, including a direct treatment of the effect of curvature through modification of the Gibbs free energy. An optimization strategy was developed to minimize the computational cost. The model was used to simulate ageing heat treatment at 600 °C of Ni-7.56 at.% Al-8.56 at.% Cr, which was studied experimentally by Booth-Morrison and others (Booth-Morrison C, Weninger J, Sudbrack CK, Mao Z, Noebe RD, Seidman DN. Acta Mater 2008;56:3422; Mao Z, Booth-Morrison C, Sudbrack CK, Martin G, Seidman DN. Acta Mater 2012;60:1871). The comparisons showed that the precipitation stages of γ′ precipitates are correctly captured by the numerical model. It was shown that non-diagonal diffusion coefficients substantially influence the selection of the operating tie-line and the overall transformation kinetics. With non-diagonal diffusion matrices, complex phenomena such as uphill diffusion of Cr due to the Al gradients were evidenced and explained.