The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γ domain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin's work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.