We measured directly the binding of Lys3, Lys5, and Lys7 to vesicles containing acidic phospholipids. When the vesicles contain 33% acidic lipids and the aqueous solution contains 100 mM monovalent salt, the standard Gibbs free energy for the binding of these peptides is 3, 5, and 7 kcal/mol, respectively. The binding energies decrease as the mol% of acidic lipids in the membrane decreases and/or as the salt concentration increases. Several lines of evidence suggest that these hydrophilic peptides do not penetrate the polar headgroup region of the membrane and that the binding is mainly due to electrostatic interactions. To calculate the binding energies from classical electrostatics, we applied the nonlinear Poisson-Boltzmann equation to atomic models of the phospholipid bilayers and the basic peptides in aqueous solution. The electrostatic free energy of interaction, which arises from both a long-range coulombic attraction between the positively charged peptide and the negatively charged lipid bilayer, and a short-range Born or image charge repulsion, is a minimum when approximately 2.5 A (i.e., one layer of water) exists between the van der Waals surfaces of the peptide and the lipid bilayer. The calculated molar association constants, K, agree well with the measured values: K is typically about 10-fold smaller than the experimental value (i.e., a difference of about 1.5 kcal/mol in the free energy of binding). The predicted dependence of K (or the binding free energies) on the ionic strength of the solution, the mol% of acidic lipids in the membrane, and the number of basic residues in the peptide agree very well with the experimental measurements. These calculations are relevant to the membrane binding of a number of important proteins that contain clusters of basic residues.