The　electronic　structure　and　magnetic　properties　of　the　M2CoA　type　Heusler　alloys　Mn2CoAl,　Mn2CoSi,　Ti2CoAl　and　Ti2CoSi　were　systematically　investigated　using　first-principles　calculations　based　on　the　density　functional　theory.　The　results　show　that　Mn2CoAl　is　a　ferrimagnetic　spin　gapless　semiconductor;　Mn2CoSi　and　Ti2CoAl　are　ferrimagnetic　spin　half-metals,　while　Ti2CoSi　is　a　ferromagnetic　spin　half-metal.　The　total　spin　magnetic　moments　of　the　M2CoA　type　Heusler　alloys　are　integers,　obeying　the　Slater-Pauling　rule.　By　analyzing　the　band　structures　and　electronic　density　of　states,　the　origin　of　spin　gapless　semiconductor　as　well　as　half-metal　were　revealed.　The　calculation　results　of　phonon　dispersion　curves　and　elastic　constants　show　that　all　the　M2CoA　type　Heusler　alloys　are　stable　in　the　lattice　dynamics　and　mechanics.　©　2016,　Beijing　University　of　Aeronautics　and　Astronautics　(BUAA).　All　right　reserved.