Lipid peroxidation is a degenerative oxidative process that modifies the structure of membranes, influencing their biological functions. Lignans, natural polyphenolic antioxidants widely distributed in plants, can prevent this membrane damage by free-radical scavenging. Here, we rationalize the difference in lipid peroxidation inhibition activity of argenteane, a natural dilignan isolated from wild nutmeg, and 3,3'-dimethoxy-1,1'-biphenyl-2,2'-diol, which represents the central part of argenteane responsible for its antioxidant activity. Although both compounds have the same capacity to scavenge free radicals, argenteane is a more active inhibitor of lipid peroxidation. We show that both compounds penetrate into DOPC and PLPC lipid bilayers and adopt similar positions and orientations, which therefore does not explain the difference in their lipid peroxidation inhibition activity. However, free energy profiles indicate that argenteane has a significantly higher affinity to the lipid bilayer, and thus a higher effective concentration to scavenge radicals formed during lipid peroxidation. This finding explains the higher activity of argenteane to inhibit lipid peroxidation.