We discuss the XXZ spin chain with certain boundary term and the representation of quantum group SUq(2). It is shown that Bethe Ansatz states are highest weight states of SUq(2), with q arbitrary We construct the irreducible representation of the quantum group. For q a rational root of unity, we show that there are new solutions to the BA equations, We derived the state vectors | b′> by taking certain limit, from which we construct the type I and type Ⅱ representations of SUq(2).