Using all-atom explicit water model and replica exchange molecular dynamics, we study the interactions between A beta monomer and nonsteroidal anti-inflammatory drug ibuprofen, which is known to reduce the risk of Alzheimer's disease. Ibuprofen binding to A beta is largely governed by hydrophobic effect, and its binding site in A beta peptide is entirely composed of hydrophobic amino acids. Electrostatic interactions between negatively charged ibuprofen ligands and positively charged side chains make a relatively small contribution to binding. This outcome is explained by the competition of ligand-peptide electrostatic interactions with intrapeptide salt bridges. Consistent with the experiments, the S-isomer of ibuprofen binds with stronger affinity to A beta than the R-isomer. Conformational ensemble of A beta monomer in ibuprofen solution reveals two structured regions, 19-25 (R1) and 29-35 (R2), composed of turn/helix and helix structure, respectively. The clustering technique and free energy analysis suggest that A beta conformational ensemble is mainly determined by the formation of Asp23-Lys28 salt bridge and the hydrophobic interactions between RI and R2. Control simulations of A beta peptide in ligand-free water show that ibuprofen binding changes A beta structure by promoting the formation of helix and Asp23-Lys28 salt bridge. Implications of our findings for A beta amyloidogenesis are discussed.