Concrete cover cracking induced by corrosion of steel reinforcement is a major influencing factor for durability and serviceability of reinforced concrete structures. In order to investigate the cracking process of concrete cover induced by rebar corrosion, the heterogeneity of concrete meso-structure and non-uniformity of rebar corrosion are accounted for. The undamaged concrete is assumed to be a three-phase composite material composed of aggregate, mortar matrix and the interfacial transition zone (ITZ). And a concrete random aggregate structure is established for the study on the mechanical behavior of the non-uniform radial corrosion expansion. In the present simulations, non-uniform radial displacement is adopted to simulate the non-uniform corrosion of the rebar; the plasticity damaged model is used to describe the mechanical behavior of the mortar matrix and the ITZ, and the aggregate is assumed to be elastic. The cracking of concrete cover due to the non-uniform corrosion of the middle located rebar is numerically simulated. The comparison of the analysis and the test result on failure pattern of cover concrete shows fairly good agreement. And then the failure patterns under uniform corrosion and non-uniform corrosion obtained from the macro-scale homogeneous model and the meso-scale heterogeneous model are compared. Furthermore, the influences of concrete cover thickness and rebar diameter on the failure pattern of concrete cover, the expansive pressure and the corrosion rate of the rebar when cover concrete cracks are investigated.