The　thermodynamics　of　five　Al3Er　compounds　were　investigated　through　first-principles　density-functional　theory　(DFT)　and　experimental　analysis.　The　Al3Er　compounds　with　Al3Ho.hR20　(prototype　Al3Ho,　Pearson　symbol　hR20),　Cu3Au.cP4,　AlNd(3.)hP8,　Ni3Ti.hP16　and　Al3Gd.hR12　structures　exhibited　formation　energies　of　-0.412(-0.417),　-0.411(-0.416),　-0.400(-0.413),　-0.399(-0.345)　and　-0.342(-0.345)　meV/atom　when　using　DFT　with　＂standard＂　potential　(＂frozen　core＂　potential)　of　Er.　The　results　indicated　that　the　Al3Ho.hR20　structure　was　the　thermodynamic　stable　phase　and　the　other　structures　were　metastable.　The　formation　energy　of　Cu3Au.cP4　structure　was　only　1　meV/atom　less　than　that　of　Al3Ho.hR20.　Experimentally,　the　Al-30　wt.%　Er　alloys　were　cooled　from　900　degrees　C　to　500　degrees　C　at　the　rate　of　5　+/-　2　degrees　C/h　and　60　+/-　2　degrees　C/h,　respectively.　The　corresponding　XRD　analysis　showed　that　the　Al3Ho.hR20　was　formed　at　the　cooling　rate　of　5　+/-　2　degrees　C/h　and　the　Cu3Au.cP4　was　formed　at　the　cooling　rate　of　60　+/-　2　degrees　C/h,　which　indicated　that　the　Al3Ho.hR20　was　in　a　thermodynamic　stable　phase　and　the　Cu3Au.cP4　was　in　a　metastable　phase　with　high　stability.　The　structural　analysis　indicated　that　the　tiny　energy　difference　between　Al3Ho.hR20　and　Cu3Au.cP4　might　be　attributed　to　a　similar　structure　with　varied　stacking　sequences.