This paper presents a mesoscopic discrete modeling approach for studying compression and fracture behavior of concrete. A modified piecewise linear sieve curve was proposed to generate irregularly shaped aggregates following specific particle size distributions, and then a random particle model and the parallel bond model were implemented within a 3D framework of discrete element model (DEM). To characterize the interface transition zone (ITZ) which is generally the weak region in concrete, a reduction factor was employed to adjust the strength and consider the effect of ITZ on the mechanical response of concrete. The numerical modeling was calibrated and validated by comparing simulation results with experimental data from compression, splitting tensile, and dog-bone tests. The results demonstrate that the random aggregate model provides accurate representations of the concrete mesostructure, and the discrete model can effectively capture the effects of aggregate size distribution and ITZ on mechanical properties and crack propagation of concrete.