Micro-electro-mechanical　system　(MEMS)　gyroscope　is　an　important　sort　of　inertial　sensor　for　measuring　the　angular　velocity　of　spinning　structures,　which　has　been　extensively　applied　in　various　engineering　areas　used　for　guidance,　location　and　motion　control.　In　this　paper,　an　improved　design　of　MEMS　vibratory　ring　gyroscope　is　proposed,　in　which　a　thin　layer　of　piezoelectric　film　(PZF)　is　introduced　encircling　the　circumferential　surface　of　the　ring,　aiming　to　modify　the　rigidity　of　the　gyroscope.　The　ring　and　the　PZF　are　both　driven　by　direct　in　conjunction　with　alternating　voltages.　The　coupled　differential　equations　governing　the　drive　and　sense　motions　are　established　via　the　Lagrangian　equations.　The　forced　responses　to　the　periodic　electrostatic　action　are　obtained　and　the　effects　of　the　drive　bias　voltage,　piezoelectric　voltage　and　spinning　speed　are　discussed.　Numerical　example　demonstrates　that　the　employment　of　PZF　can　greatly　enhance　the　gyroscope　sensitivity.　Parametric　vibration　of　the　gyroscope　due　to　periodically　varying　rigidity　induced　by　the　periodic　piezoelectric　voltage　is　also　investigated.　The　stability　regions　of　the　system　are　acquired　by　using　the　multiple　scales　method,　and　the　effect　of　the　piezoelectric　voltage　is　analyzed.　The　results　show　that　the　attached　PZF　can　also　enhance　the　gyroscope　sensitivity　by　the　generated　parametric　resonance.