The　solubility　curves　of　Er　in　Al-Er　alloys　were　obtained　by　first　principles　calculations　based　on　the　density　functional　theory.　The　solution　energies　of　Er　atoms　in　these　Al-Er　alloys　were　calculated　using　the　＂frozen　core＂　approximation　and　＂standard　potential＂　approximation　for　the　4f　electrons.　The　calculated　results　show　that　the　solution　energies　of　hR20,　cP4　and　hP8-Al3Er　are　-1.003　and　-0.767　eV/Er　atom,　-0.987　and　-0.757　eV/Er　atom,　-0.967　and　-0.713　eV/Er　atom,　respectively,　obtained　from　the　two　approximations.　The　lattice　dynamics　calculation　shows　that　the　excess　enthalpies　of　hR20,　cP4　and　hP8-Al3Er　are　3.301,　3.229　and　3.309　kB/Er　atom.　The　simulated　solubility　curves　were　obtained　by　combining　the　lattice　dynamics　values　and　the　weighted　average　of　the　solution　energy　values.　The　calculated　solubility　curves　of　cP4-Al3Er　are　consistent　with　the　experimental　values,　which　indicates　that　the　4f　electrons　play　a　very　important　role.　In　addition,　the　solubility　curve　of　cP4-Al3Er　is　very　close　to　that　of　the　hR20-Al3Er,　but　lower　than　that　of　hP8-Al3Er　at　the　same　temperature.　The　chemical　driving　forces　corresponding　to　the　solubility　curves　of　hR20　and　cP4-Al3Er　are　also　close　to　each　other,　but　larger　than　that　of　the　hP8-Al3Er.　Due　to　the　smaller　interfacial　energy　in　Al　matrix　of　cP4-Al3Er　than　that　of　hR20-Al3Er,　it　could　be　deduced　that　the　cP4-Al3Er　precipitation　is　the　first　in　priority　order,　which　is　consistent　with　the　experimental　observations.　©　2020,　Science　Press.　All　right　reserved.