In order to study the damage evolution process of mesoscopic structure and macro-mechanical properties of concrete under uniaxial load, it conducts numerical experiment to analyze the macro-mechanical properties of uniaxial damage of cubic concrete specimen with three grain-size levels by applying Marazs damage model to describe constitutive relation of concrete materials. The numerical experiment results show that the damage of concrete specimen under uniaxical load fracture resulted from the continuous accumulation and evolution of internal initial damge, the final failure pattern of numerical experiments is basically similar to the damage form from the micro level, the aggregate distribution, the thickness of adhesive layer, adhesive layer and matrix strength have a certain impact on concrete maceoscopic damage, it shows that the method is reasonable and reliable for the analysis of the failure mechanism of conerete mesoscopic structure.