The　crystal　structure　and　Raman　spectra　of　quartz　are　calculated　by　using　first-principles　method　in　a　pressure　range　from　0　to　5　GPa.　The　results　show　that　the　lattice　constants　(a,　c,　and　V)　decrease　with　increasing　pressure　and　the　a-axis　is　more　compressible　than　the　c　axis.　The　Si-O　bond　distance　decreases　with　increasing　pressure,　which　is　in　contrast　to　experimental　results　reported　by　Hazen　et　al.　[Hazen　R　M,　Finger　L　W,　Hemley　R　J　and　Mao　H　K　1989　Solid　State　Communications　725　507-511],　and　Glinnemann　et　al.　[Glinnemann　J,　King　H　E　Jr,　Schulz　H,　Hahn　T,　La　Placa　S　J　and　Dacol　F　1992　Z.　Kristallogr.　198　177-212].　The　most　striking　changes　are　of　inter-tetrahedral　O-O　distances　and　Si-O-Si　angles.　The　volume　of　the　SiO44-　tetrahedron　decreased　by　0.9%　(from　0　to　5　GPa),　which　suggests　that　it　is　relatively　rigid.　Vibrational　models　of　the　quartz　modes　are　identified　by　visualizing　the　associated　atomic　motions.　Raman　vibrations　are　mainly　controlled　by　the　deformation　of　the　SiO44-　tetrahedron　and　the　changes　in　the　Si-O-Si　bonds.　Vibrational　directions　and　intensities　of　atoms　in　all　Raman　modes　just　show　little　deviations　when　pressure　increases　from　0　to　5　GPa.　The　pressure　derivatives　(d　nu(i)/dP)　of　the　12　Raman　frequencies　are　obtained　at　0　GPa-5　GPa.　The　calculated　results　show　that　first-principles　methods　can　well　describe　the　high-pressure　structural　properties　and　Raman　spectra　of　quartz.　The　combination　of　first-principles　simulations　of　the　Raman　frequencies　of　minerals　and　Raman　spectroscopy　experiments　is　a　useful　tool　for　exploring　the　stress　conditions　within　the　Earth.