Quantum phase slips can induce a phase transition in a single Josephson junction by varying coupling strength Rs to the dissipative environment. We study the finite Josephson junction array with dissipations. For the infinite arrays with no dissipation, a quantum KT phase transition can occur by varying the ratio of the Josephson coupling strength Ej to the charging energy E c due to the unbinding of instanton pairs. At finite temperature and array size, there will be a rich interplay between instantons and quantum phase slips.