Weibel　instability　in　plasma,　where　the　ion　distribution　is　isotropic　and　the　electron　component　of　the　plasma　possesses　the　anisotropic　temperature　distribution,　is　investigated　based　on　the　kinetic　theory　in　context　of　nonextensive　statistics　mechanics.　The　instability　growth　rate　is　shown　to　be　dependent　on　the　nonextensive　parameters　of　both　electron　and　ion,　and　in　the　extensive　limit,　the　result　in　Maxwellian　distribution　plasma　is　recovered.　The　instability　growth　rate　is　found　to　be　enhanced　as　the　nonextensive　parameter　of　electron　increases.　(C)　2013　AIP　Publishing　LLC.