In order to investigate the influences of initial defects, such as the internal tiny cracks, on the concrete strength, concrete was considered to be a four-phase composite composed of coarse aggregate, mortar matrix, interfacial transitional zones(ITZs), and initial interfacial defects at the meso-level, and a numerical model for mesoscale modeling of concrete, considering initial interfacial defects, was developed to predict the uniaxial tensile strength of concrete. The influences of the initial interfacial defect distribution and the amount of defects on the uniaxial tensile strength of concrete are discussed. Results show that the initial interfacial defect distribution has little influence on the uniaxial tensile strength, while the amount of initial interfacial defects has a large influence on the concrete strength. Results also indicate that the uniaxial tensile strength decreases with the increase of the amount of initial interfacial defects. When the volume fraction of initial interfacial defects in the transition zone increases from 10% to 50%, the uniaxial tensile strength of samples in comparison to the strength of samples without defects decreases from 94% to about 60%.