Let \(B_k=\{x\in \mathbb R^n\); \(| x| \leq 2^k\}\) and \(C_k=B_k \setminus B_{k-1}\) for \(k\in \mathbb Z\). Let \(\chi_k\) denote the characteristic function of the set \(C_k\). Suppose \(00)\). The authors give the boundedness theorem of the Calderón-Zygmund operator of type \(\delta\) on these Hardy spaces of weighted Herz type, and an interpolation theorem of linear operators on the weighted Herz spaces.