Experiments have shown that charged nanoparticles (NP) inhibit, partially or completely, the aggregation of Aβ protein monomers into fibrils. The equilibrium fibril content is found to be inversely proportional to the concentration of NP. In this work, we report a kinetic model for the fibrillation of Aβ protein in the presence of NP. In the model, apart from nucleation, elongation and fragmentation processes, the effect of NP is considered to cause a conformational change to the protein monomer, making the latter incompatible for aggregation. The simulated results explain the growth kinetics of pure Aβ (1-40) protein, and the kinetics in the presence of NP. The NP-monomer interaction considered in the model captures the significant effect of NP on the fibrillation process at a very molar ratio (NP to Aβ monomer) as low as 10. The model predictions are compared with two different NP systems, namely, gold and silica NP. The model can be applied to explain the inhibitory effect of other additives such as small molecules, NP, lipids, and surfactants that show a similar inhibition trend for fibril formation of Aβ and other proteins.