An inverse spectra problem which has an important significance in the control field is discussed, that is, find an irreducible tridiagonal quaternion matrix T, such that T has the given distinct nonzero eigenvalues {Λ,}" =3D1 and a right eigenpairs (λα). In this paper, we use inverse Arnoldi algorithm for an unitary similarity matrix and construct the appropriate similarity transformation, an irreducible tridiagonal quaternion matrix T with given conditions is obtained. At the same time, two numerical examples checks the method's feasibility and precision.