Geodesic　acoustic　mode　(GAM)　in　collisionless　toroidal　plasmas　with　a　constant　electrostatic　potential　around　a　magnetic　surface　is　investigated　based　on　the　linear　gyrokinetic　theory　in　context　of　nonextensive　statistics　mechanics.　The　damping　rate　of　GAM　is　shown　to　be　dependent　on　the　nonextensive　parameters　of　ions,　and　in　the　extensive　limit,　the　result　in　Maxwellian　distribution　plasma　is　recovered.　The　damping　rate　is　found　to　be　enhanced　as　the　nonextensive　parameter　of　ion　decreases.　(C)　2014　AIP　Publishing　LLC.