The additive manufacturing process unique characteristics lead to the formation of structures with varying mechanical properties in different directions. However, current topology optimization methods often assume material isotropy, overlooking the anisotropy additive manufacturing materials. Hence, we propose a topology optimization method that accounts for additive manufacturing material anisotropy. We establish a local coordinate system to describe material anisotropy and integrate it into the SIMP variable density method, deriving the corresponding interpolation formula. The Kuhn-Tucker condition optimization criterion is applied to solve the problem, and an optimization program is developed. The method's feasibility and effectiveness are validated through numerical examples, and we extensively discuss the impact of material anisotropy and printing direction on topology optimization results. Research demonstrates that our proposed method is adept at solving both isotropic and anisotropic topology optimization problems. Moreover, the material degree of anisotropy and printing direction significantly influence topology optimization outcomes. Accounting for material anisotropy, the maximum principal stress difference in optimization results obtained under different printing directions can reach 52.26%.