It is essential to explore the corrosion cracking of concrete under sulfate attack to predict the service performance and durability of concrete structures. The damage degree of concrete caused by sulfate attack is quantitatively investigated. Based on the damage mechanism of the local cracking stage, a chemo-micromechanical damage model of sulfate attack of concrete is established by elasto-damage mechanics. The progressive degradation behavior of concrete under sulfate attack is divided into three zones, including the chemical corrosion zone, the damaged concrete zone by expansive stress, and the intact concrete zone. The proposed chemo-micromechanical damage model can quantitatively determine the effects of chemical sulfate corrosion on mechanical properties of concrete. In addition, the present model considers the interaction among corrosion products, the damaged concrete, the intact concrete and uncorrupted hydration products. The comparison between the calculation results and the available experimental data shows that the proposed model is feasible for corrosion cracking analysis. Based on the proposed model, the influencing factors of concrete damage are discussed. With the increase of corrosion degree, the content of corrosion products, the expansion coefficient of corrosion products and the initial radius of corrosion products, the elastic moduli of concrete decrease after sulfate attack. When the tensile strength and rigidity of concrete matrix reduce, the effective elastic moduli of concrete after sulfate attack also deteriorate. The numerical results exhibit that the proposed chemo-micromechanical model is of notable significance to the application of the chemo-mechanical coupling problems of cementitious composite materials.