A　temperature　acquisition　system　was　used　to　measure　average　solidification　cooling　rate　of　GE81　alloys　under　different　cooling　conditions,　including　furnace-cooling　in　graphite　mold,　air-cooling　in　graphite　mold,　air-cooling　in　steel　mold　and　air-cooling　in　copper　mold.　The　relationship　between　cooling　rate　and　grain　density　was　studied　based　on　classical　nucleation　theory.　Optical　microscope　(OM)　and　scanning　electron　microscope　(SEM)　were　used　to　observe　the　microstructure　of　as-cast　GE81　alloys　(Mg-8Gd-1Er,　wt%)　at　various　cooling　rates　in　order　to　establish　the　relationship　between　solidification　cooling　rate,　grain　density,　hardness　and　volume　fraction　of　secondary　phases.　The　results　show　that　the　solidification　cooling　rates　of　GE81　alloy　in　the　four　moulds　are　0.23,　0.46,　2.17　and　3.88　K•s-1,　respectively.　The　cooling　rate　is　linear　with　the　undercooling,　and　the　formula　is　∆T=13.5664v+6.9655.　With　the　increasing　cooling　rate,　the　α-Mg　grains　are　refined　obviously.　The　relationship　between　the　cooling　rate　and　the　grain　density　can　be　described　as　Nv=1.1135×1012exp(-46.8344/(13.5664v+6.9655)).　Moreover,　the　secondary　phase　distribution　is　more　homogeneous　and　their　volume　fraction　decreases　so　that　the　hardness　of　the　GE81　alloy　increases　significantly.　The　relationship　between　the　hardness　and　the　cooling　rate　can　be　expressed　as　HV=72.1772-12.6895/(1+exp(v-2.2570)).　©　2018,　Science　Press.　All　right　reserved./Copyright　©　2018,　Northwest　Institute　for　Nonferrous　Metal　Research.　Published　by　Elsevier　BV.　All　rights　reserved.