Binding of curcumin, naproxen, and ibuprofen to Aβ1-40 peptide and its fibrils is studied by docking method and all-atom molecular dynamics simulations. The Gromos96 43a1 force field and simple point charge model of water have been used for molecular dynamics simulations. It is shown that if the receptor is a monomer then naproxen and ibuprofen are bound to the same place that is different from the binding position of curcumin. However all of three ligands have the same binding pocket in fibrillar structures. The binding mechanism is studied in detail showing that the van der Waals interaction between ligand and receptor dominates over the electrostatic interaction. The binding free energies obtained by the molecular mechanic-Poisson-Boltzmann surface area method indicate that curcumin displays higher binding affinity than nonsteroidal anti-inflammatory drugs. Our results are in good agreement with the experiments.