A　high-sensitivity　fiber　Bragg　grating　(FBG)　pressure　sensor　has　been　designed　and　studied.　Confining　some　gas　inside　a　glass　cylinder　with　a　close　glass　piston　which　can　move　smoothly　along　the　cylinder,　and　sticking　two　ends　of　a　fiber　Bragg　grating　on　the　outer　side　of　the　cylinder　and　piston　respectively.　The　variation　of　the　external　pressure　results　in　the　change　of　the　tension　that　the　fiber　grating　is　subjected　to　and　then　the　pressure　can　be　measured　by　the　measurement　of　the　Bragg　wavelength　of　the　FBG.　The　pressure　sensitivity　coefficient　is　up　to　-0.7676/MPa,　which　is　about　3.88x10(5)　times　the　value　of　bare　fiber　Bragg　gratings,　the　highest　sensitivity　ever　reported.　The　sensor　can　be　used　to　potential　applications　in　the　measurement　of　air　pressure,　hydraulic　pressure　and　vibration　in　the　range　of　low　pressure.