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In this paper we develop an immersed interface finite element method for a kind of anisotropy diffusion models governed by the elliptic interface problems with discontinuous tensor-coefficients. The method is based on linear polynomials on non-interface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.