In this paper, a class of constrained inverse eigenproblem and associated approximationproblem for skew symmetric and centrosymmetric matrices are essentially decomposed intothe same kind subproblems for real antisymmetric matrices with smaller dimensions.We presentthe general solution of the constrained inverse eigenproblem for skew symmetric andcentrosymmetric matrices in real number field. In addition, in corresponding solution set ofthe constrained inverse eigenproblem for skew symmetric and centrosymmetric matrices, theexplicit expression of the nearest matrix to a given matrix in the Frobenius norm is obtained.