The temperature below which the homogeneous liquid state of a mixture is not thermodynamically stable is called the liquidus temperature. This temperature varies with composition, and its composition dependence is represented by the liquidus curve. This curve provides fundamental reference points on the composition-temperature plane for characterizing the behavior of liquids, glasses, and crystals. In this paper, using molecular dynamics simulations, we determine the liquidus curve of the Wahnström mixture, which consists of large and small atoms interacting via the Lennard-Jones potential. Since this system is one of the standard models used to study the behavior of liquids and glasses, the liquidus curve presented in this work will contribute to a deeper understanding of disordered materials in general.