The interaction of a potassium ion with a dimyristoyl phosphatidylcholine (DMPC) bilayer membrane is investigated using molecular dynamics calculations based on a detailed atomic model. Umbrella sampling calculations are performed to obtain the ion-bilayer potential of mean force near the membrane-solution interface. The solvation shell around the K+ changes progressively through the interfacial polar head group region. Direct association of the ion with the phosphate and carbonyl lipid groups is observed, replacing a water molecule from the first hydration shell. On average, the ion is in close contact with 7 or 8 oxygen ligands. The potential of mean force is compared with the results of continuum electrostatic calculations.