The　fundamental　aspects　of　temperature-　and　composition-dependent　site　preference　of　alloying　elements　on　sublattice　of　Co3Al-based　gamma　＇　phase　with　L12　structure　have　not　been　well　understood,　which　hinders　the　design　of　advanced　Co-based　high-temperature　alloys.　In　this　work,　the　temperature-　and　composition-dependent　site　preferences　of　the　binary,　ternary,　and　quaternary　Co3Al-based　gamma　＇　phase　alloyed　with　Mi　were　studied　using　a　two-sublattice　thermodynamic　involving　site　occupying　fractions　(SOFs).　The　SOFs　were　calculated　using　a　thermodynamic　software　package　based　on　a　thermodynamic　database　established　in　this　work,　where　the　temperature-dependent　thermodynamic　data　were　obtained　using　first-principles　calculations　based　on　densityfunctional　theory　(DFT)　and　density-functional　perturbation　theory　(DFPT).　The　additional　alloying　elements　Mi　added　represent　the　transitional　metals　Cr,　Cu,　Fe,　Mn,　Mo,　Ni,　Re,　Ta,　Ti,　V,　or　W　(arranged　in　alphabetical　order).　The　results　show　that　there　is　an　obvious　order-disorder　transition　for　the　stoichiometric　and　nonstoichiometric　binary　Co3Al　as　well　as　in　ternary　and　quaternary　Co3Al-based　systems　alloyed　by　adding　additional　transition　metals　around　the　solvus　temperature.　For　the　stoichiometric　Co3Al　gamma　＇　phase,　the　critical　temperature　is　about　1073　K,　accompanied　with　the　site　configuration　changes　from　(Al)1a(Co)3c　at　room　temperature　to　(Al0.2590Co0.7409)1a　(Al0.2469Co0.7530)3c　at　1273　K,　while　this　order-disorder　transition　was　not　found　in　the　Ni3Al-based　gamma　＇　phase,　a　counterpart　of　Co3Al-based　gamma　＇　phase.　When　xCo/xAl　is　over　3:1,　for　example,　the　non-stoichiometric　Co3Al-based　binary　gamma　＇　phases　78Co-22Al　show　continuously　order-disorder　transition　characteristics　with　a　broadened　transition　temperature　range.　For　the　gamma　＇　phase　with　the　composition　78Co-26Al4　Mi　which　is　normalized　as　72.22Co-24.08Al-3.7　Mi　(at%),　where　we　kept　xCo/xAl　=　3:1　to　study　the　ordering　behaviors　of　the　additional　alloying　transition　metals　Mi　conveniently.　It　is　revealed　that　Cu,　Fe,　Mn,　and　Ni　atoms　always　prefer　the　3c　sublattice　(Co　site),　and　Mo,　Ta,　Ti,　and　W　atoms　always　prefer　the　1a　sublattice　(Al　site)　in　the　whole　temperature　range,　while　the　site　preferences　of　Cr,　Re,　and　V　atoms　are　affected　by　the　heat　treatment　temperature.　For　example,　when　the　heat　treatment　temperature　is　lower　than　700　K,　Cr　and　V　atoms　randomly　occupy　1a　and　3c　sublattice,　and　Re　atoms　prefer　to　3c　sublattice,　while　when　the　heat　treatment　temperature　is　higher　than　1273　K,　Cr　atoms　prefer　3c　sublattice,　V　atoms　prefer　to　1a　sublattice,　and　all　Re　atoms　occupy　3c　sublattice　exclusively.　The　site　preference　of　the　quaternary　system　with　a　selective　composition　78Co-26Al-2　M1-2　M2,　which　is　normalized　as　72.22Co-24.08Al-1.85　M1-1.85　M2　(at%)　has　been　also　investigated.　The　additional　alloying　transition　metals　Mi　added　modulate　the　order-disorder　transition　characteristics　of　Co3Al-based　gamma　＇-precipitate　with　different　amplitudes.　The　order-disorder　transition　temperatures　for　some　selected　alloys　were　verified　experimentally　using　DSC.　Based　on　the　causal　relationship　of　structure　and