In this study, we characterize a new class of Arf numerical semigroups in the form of S={0,an-2t, (an-2t+ an-3)t,…,( an-2+…+a0+1)t,→…} for a ≥ 2, aϵ Z. We give some invariants of this class as Frobenius number, genus and Apery set and we obtain some results about these concepts.