In　this　study,　a　parametric　amplification　model　of　a　vibrating　beam　micro-gyroscope　is　established　with　the　effects　of　size-dependent　and　fringing　field　taken　into　account.　Compared　with　conventional　electrostatic　beam　gyroscopes,　piezoelectric　films　are　added　to　the　four　surfaces　of　the　rectangular　beam　of　vibrating　micro-gyroscopes.　Due　to　piezoelectric　effect,　the　beam　will　be　subjected　to　an　axial　excitation,　which　provides　parametric　amplification　to　enlarge　the　transverse　vibration　and　to　enhance　the　sensitivity.　The　effects　of　the　size-dependent,　fringing　field　and　piezoelectric　voltages　on　static　deflection,　eigenvalue　analysis　and　dynamic　amplification　of　the　vibrating　beam　micro-gyroscopes　are　investigated.　The　influence　of　damping　on　the　stability　analysis　of　the　gyroscopic　system　is　also　studied.　When　the　frequency　of　parametric　excitation　is　twice　the　natural　frequency　of　the　system,　it　is　found　that　higher　piezoelectric　AC　voltage　amplitudes　within　the　stable　region　are　given　in　both　sense　and　drive　directions,　which　may　generate　a　better　sensitivity　of　the　vibrating　beam　micro-gyroscope.　(C)　2020　Elsevier　Inc.　All　rights　reserved.