A　meshing　model　of　cycloid　bevel　gear　was　established,　considering　the　effect　of　friction　and　parameter　excitation.　The　relative　displacements　along　the　line　of　action　of　gear　meshing　point　was　taken　as　generalized　coordinates,　the　torsional　vibration　equation　of　pinion　and　gear　was　obtained　by　using　Lagrange　principle,　and　then　the　system　dynamics　equation　was　derived　through　order　reduction,　decoupling　and　normalization.　Adopting　fourth-fifth　order　Runge-Kutta　method　to　solve　the　dynamic　equation,　the　curve　of　the　displacement　response　at　tooth　meshing　point　versus　friction　factor　was　given.　Under　system　parameter　excitation,　the　influences　of　damping　level,　external　load,　transmission　error,　stiffness　and　excitation　frequency　on　vibration　characteristics　of　meshing　point　were　analysed　with　and　without　consideration　of　friction　effect　respectively.　The　displacement　response　curves　corresponding　to　parameter　excitation　were　also　presented.　The　simulation　results　show　that:　the　displacement　response　amplitude　at　meshing　point　under　parametric　excitation　is　effectively　restrained　by　friction,　the　peak　frequency　drifts　and　the　excitation　frequency　and　the　friction　can　both　change　the　motion　behavior　and　increase　the　complexity　of　system　movement.