Abstract: Concrete is the most widely used construction material and composed of mortar, aggregates and, interface transition zone on the mesoscale. Building 3D mesoscale models is an important method for investigating inner damage mechanism of concrete material under loadings. Randomly distributed convex polyhedron aggregates of random shapes and dimensions are modeled upon the conventional “take-and-place” method, and the control of aggregate volume fraction within 50% is realized by simulating the gravitational drop and by the shrinkage of aggregates; Polyhedron aggregates are meshed with tetrahedral elements to represent their actual shapes. Besides, ITZ is represented by cohesive contact which equals to zero-thickness cohesive elements to erase the difficulty in the mesh of ITZ with thickness of 20 μm~50 μm; RHT model is employed for mortar and aggregates and then the concrete 3D mesoscale finite element model is established. Subsequently, the numerical simulations are conducted for the mechanical behavior of concrete under uniaxial compression, uniaxial tension, splitting tension, biaxial loading and triaxial compression. The reliability of the concrete 3D mesoscale finite element model is proved by comparing simulated stress-strain curves and failure patterns with experimental results. The effects of mortar strength, aggregate strength, ITZ strength, aggregate size and aggregate volume fraction on the mechanical behavior of concrete under uniaxial compression are investigated. The increase of mortar strength causes the significant increase of concrete strength, while the effects of aggregate strength and ITZ strength are small. Besides, the concrete peak strain increases significantly with the increase of mortar and ITZ strength and decreases slightly with the increase of aggregate strength. With the decrease of aggregate volume fraction and the increase of aggregate size, concrete strength increases slightly and peak strain decreases.