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Let Ω ∈ Ls(Sn-1) (s ＞ 1) be a homogeneous function of degree zero and b be a BMO function or Lipschitz function.In this paper,the authors obtain some boundedness of the Calderón-Zygmund singular integral operator TΩ and its commutator [b,TΩ] on Herz-Morrey spaces with variable exponent.