A　nonlinear　vibration　analysis　of　a　simply　supported　functionally　graded　rectangular　plate　with　a　through-width　surface　crack　is　presented　in　this　paper.　The　plate　is　subjected　to　a　transverse　excitation　force.　Material　properties　are　graded　in　the　thickness　direction　according　to　exponential　distributions.　The　cracked　plate　is　treated　as　an　assembly　of　two　sub-plates　connected　by　a　rotational　spring　at　the　cracked　section　whose　stiffness　is　calculated　through　stress　intensity　factor.　Based　on　Reddy＇s　third-order　shear　deformation　plate　theory,　the　nonlinear　governing　equations　of　motion　for　the　FGM　plate　are　derived　by　using　the　Hamilton＇s　principle.　The　deflection　of　each　sub-plate　is　assumed　to　be　a　combination　of　the　first　two　mode　shape　functions　with　unknown　constants　to　be　determined　from　boundary　and　compatibility　conditions.　The　Galerkin＇s　method　is　then　utilized　to　convert　the　governing　equations　to　a　two-degree-of-freedom　nonlinear　system　including　quadratic　and　cubic　nonlinear　terms　under　the　external　excitation,　which　is　numerically　solved　to　obtain　the　nonlinear　responses　of　cracked　FGM　rectangular　plates.　The　influences　of　material　property　gradient,　crack　depth,　crack　location　and　plate　thickness　ratio　on　the　vibration　frequencies　and　transient　response　of　the　surface-racked　FGM　plate　are　discussed　in　detail　through　a　parametric　study.