The migration of harmful chemicals from food contact materials is a major pathway for food contamination and poses significant risks to human health. Molecular dynamics simulations were used to construct a single-phase low-density polyethylene/butylated hydroxyanisole (LDPE/BHA) model and a two-phase LDPE/BHA-food simulant model. The diffusion behavior of BHA molecules at four temperatures (278, 298, 310, and 333 K) was investigated using mean square displacement analysis. Furthermore, the diffusion mechanism of BHA molecules was explored in terms of solubility parameters, diffusion coefficients, interaction energy with LDPE, free volume fraction, solubility parameter, molecular trajectories, and the type of food simulants. The results reveal that BHA diffusion is influenced by multiple factors. At higher temperatures, the diffusion coefficients of BHA molecules increase significantly due to elevated molecular energy, an expanded free volume fraction, and enhanced segmental motion of polymer chains, which collectively provide more diffusion pathways. The strong interaction between BHA molecules and polymers results in a reduced diffusion coefficient for BHA. Food simulants with solubility parameter values similar to those of polymers facilitate the migration of BHA.