We　performed　the　first-principle　calculation　to　study　the　structures　of　cinnabar　phase　and　the　Cinnabar-to-rocksalt　Phase　transitions　of　HgTe　and　CdTe　under　high　pressure.　The　calculated　results　show　that　for　HgTe,　the　zincblende-to-cinnabar　phase　transition　is　under　2.2GPa,　and　the　cinnabar-to-rocksalt　phase　transition　is　under　5.5　GPa;　For　CdTe,　the　two　phase　transitions　occur　under　4.0　GPa　and　4.9　GPa,　respectively,　which　well　agree　with　the　experimental　results.　The　cinnabar-to-rocksalt　phase　transitions　of　most　compounds,　including　HgTe　and　CdTe,　except　HgS　are　of　first-order,　and　it　is　due　to　that　their　cinnabar　phases　are　not　chain　structure　as　HgS　and　there　are　no　relaxation　process　before　the　phase　transition.　©　(2014)　Trans　Tech　Publications,　Switzerland.