We propose an integrable open XXZ chain coupled to the boundary impuri
ties with arbitrary exchange constants. The Bethe ansatz equation and
eigenvalues are obtained by using the quantum inverse scattering metho
d. The ground-state properties are discussed by solving the Bethe equa
tion in some special cases. In addition, we present an approach for co
nstructing the reflecting matrix K which produces the boundary term co
upled to impurities.