The macroscopic mechanical behaviors of concrete depend on the material composition and its properties. In this paper, a mesoscale numerical model of concrete with multiphase heterogeneity based on the band-based peridynamic theory was established to study the macroscopic mechanical properties and fracture processes of concrete under uniaxial tension. The rationality of the model was verified by varying the content of coarse aggregate, the strength of mortar, the strength of coarse aggregate and the strength of interface transition zone (ITZ). The results show that the stress-strain curves before the softening section can be reproduced well, and the mechanical properties and fracture process of concrete under uniaxial tension can be accurately described. In addition, the fracture process of different types of concrete under uniaxial tension can be reasonably simulated by adjusting the mechanical parameters of each phase materials in the numerical model.