Abstract: 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 H_2n² 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 KC₄×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.