Abstract: Macroscopic mechanical properties and failure mechanism of concrete are determined by the microscopic components. And the interface between aggregate and cement mortar is an important factor that affects the failure path and macro-mechanical properties of concrete. The interfacial transition zone is regarded as a layer of near-field mortar with a high porosity different from the far-field mortar matrix. The mechanical properties of the three-phase composite meso elements of concrete are deduced by a “two-step equivalent method”, and then the equivalent constitutive relationship of each meso element is obtained. Based on the meso element equivalent model, the damage process and the macro-mechanical properties of two-grade concrete are investigated under the loading conditions of uniaxial tension, uniaxial compression and bending. And the influence of interface-phase on the mechanical properties of concrete is discussed. Besides, the results of the present model are compared with the ones by a random aggregate model. The analysis results show that the existence of interfacial transition zone has a great influence on the macro elastic modulus, strength and residual strength of concrete, which should not be neglected when analyzing on the macro-mechanical properties and damage fracture of concrete.