The　hybrid　energy　conversion　mechanism　can　improve　the　performance　of　the　energy　harvester　compared　to　the　single　energy　conversion　mechanism.　Meanwhile,　the　use　of　viscoelastic　materials　can　also　improve　the　energy　harvesting　efficiency,　but　there　is　not　much　research　on　hybrid　energy　harvesting　systems　with　viscoelastic　material.　Different　from　existing　research,　this　manuscript　investigates　the　probabilistic　response　and　stochastic　bifurcation　of　a　hybrid　piezoelectric　and　electromagnetic　energy　harvester(HPEEH)　with　viscoelastic　term　under　random　excitation.　Firstly,　the　viscoelastic　element　is　approximately　equivalent　to　the　linear　combination　of　damping　term　and　stiffness　term　through　variable　transformation.　Secondly,　the　accuracy　of　the　proposed　method　is　verified　by　comparing　the　numerical　solution　with　the　analytical　solution　using　the　stochastic　averaging　technique　to　solve　the　equivalent　system.　Furthermore,　the　bifurcation　conditions　for　amplitude　steady-state　probability　density　are　given　according　to　the　singularity　theory　and　the　definition　of　the　extreme　point.　It　is　found　that　changes　in　viscoelastic　parameters,　damping　coefficients　and　electromagnetic　coupling　coefficients　can　induce　stochastic　P-bifurcation.　Finally,　the　effects　of　system　parameters　on　mean　square　current,　mean　square　voltage　and　mean　output　power　are　explored.　©　2022　Elsevier　Ltd