Abstract: The meso-finite element model of concrete with random three-dimensional polyhedral aggregate is firstly established by developing MATLAB and ABAQUS Python script programs. A highly efficient C++ program is then developed to insert 3D cohesive elements with zero-thickness into the aggregate-mortar interfaces and within the mortar matrix, to realistically simulate their complicated crack initiation and propagation. Parametric studies are carried out to investigate the influence of cohesive fracture properties on the load-carrying capacity and cracking process. The simulation results show that: the macroscopic stress-displacement curve is mainly affected by the tensile strength and fracture energy of mortar and interface viscous crack unit, and the position and shape of crack surface are determined by the relative ratio of tensile strength and fracture energy of mortar and interface bonded crack unit. The mechanical response of concrete reflects the characteristics of crack development, which are not only determined by fracture material parameters, but also affected by meso-structural factors such as aggregate size and shape. The meso-structural features of aggregates also have significant effects on the complicated 3D cracking process.