This　paper　investigates　vibrations　of　the　edge-cracked　functionally　graded　graphene　reinforced　composite　(FG-GRC)　beam　with　the　piezoelectric　actuators.　The　edge　crack　is　simulated　by　a　rotational　massless　spring　model.　The　effective　Young　modulus　of　the　FG-GRC　beam　is　estimated　by　utilizing　the　modified　Halpin-Tsai　model.　The　rule　of　mixture　is　applied　to　calculate　the　mass　density　and　Poisson　ratio　of　the　FG-GRC　beam.　The　total　energy　function　of　the　edge-cracked　FG-GRC　piezoelectric　beam　is　derived　through　using　Timoshenko　beam　theory　and　von　Karman　nonlinear　strain-displacement　relationship.　The　mechanical-electrical　governing　equations　of　motion　for　the　edge-cracked　FG-GRC　piezoelectric　beam　are　obtained　by　applying　the　standard　Ritz　procedure　and　are　solved　by　the　direct　iterative　method.　The　effectiveness　and　accuracy　of　this　approach　are　verified　through　comparing　the　present　results　with　other　research　results.　Both　uniformly　and　functionally　graded　(FG)　distributed　graphene　nanoplatelets　(GPLs)　are　considered　to　analyze　influences　of　the　GPL　weight　fraction,　crack　depth,　crack　location,　boundary　condition,　thickness　of　the　piezoelectric　layer,　and　applied　actuator　voltage　on　the　mechanical-electrical　linear　and　nonlinear　vibrations　of　the　edge-cracked　FG-GRC　beam.　The　numerical　results　can　help　us　predict　the　mechanical-electrical　dynamic　behaviors　of　the　FG-GRC　beam　with　cracks　and　promote　the　development　of　the　structural　health　monitoring.