Kac　and　Paljutkin　constructed　a　class　of　non-commutative　and　non-cocommutative　semisimple　Hopf　algebra　K8,　then　Masuoka　reconstructed　this　algebra　by　lifting　method.　Ore　extension　is　an　important　method　to　construct　new　examples　of　neither　commutative　nor　cocommutative　Hopf　algebras.　Many　interesting　quantum　algebras　can　be　obtained　in　this　way.　More　extensive　non-commutative　and　non-cocommutative　semisimple　Hopf　algebra　H2n2　was　constructed　by　means　of　Ore　extension.　Its　coalgebraic　multiplication　was　determined　by　the　Drinfeld　twist　element　and　some　algebraic　automorphism.　In　this　paper,　the　definition　of　a　class　of　non-commutative　and　non-cocommutative　semisimple　Hopf　algebra　H32of　dimension　32　was　given,　which　can　be　obtained　by　the　special　Ore　extension　for　the　given　K[C4×C4]　of　Abel　group　algebras　of　order　16.　It　has　a　sub-Hopf　algebra　of　dimension　8,　which　is　just　isomorphic　to　the　unique　neither　commutative　nor　cocommutative　semisimple　8-dimension　Hopf　algebra　K8.　Then,　the　main　task　was　to　study　the　quasitriangular　structure　of　the　Hopf　algebra　H32.　Through　detailed　calculation,　all　the　universal　R-matrices　for　this　class　of　Hopf　algebras　were　given.　Combining　with　Wakui＇s　conclution,　we　know　that　H8　is　a　minimal　quasitriangular　Hopf　algebra;　however,　H32　is　not.　©　2019,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.