In this paper we introduce a class of quasipolar rings which is a generalization of J-quasipolar rings. Let R be a ring with identity. An element a is an element of R is called delta-quasipolar if there exists p(2) = p is an element of comm(2)(a) such that a + p is contained in delta(R), and the ring R is called delta-quasipolar if every element of R is delta-quasipolar. We use delta-quasipolar rings to extend some results of J-quasipolar rings. Then some of the main results of J-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of delta-quasipolar rings.