Abstract: The size effect and macroscopic nonlinearity of concrete are caused by its inherent heterogeneity. Considering the mesoscopic heterogeneity, concrete was regarded as a tril-phase composite material consisting of aggregate, mortar matrix and the interfacial transition zone (ITZ) at meso-scale. Numerical concrete specimens sized by 150 mm×150 mm, 300 mm×300 mm and 600 mm×600 mm were set up. First, several uniaxial compressive tests of square concrete specimens were conducted and the mechanical parameters of the ITZs were fixed by an inversion method. Then the failure behavior and the size effect of concrete under biaxial compression were analyzed. Some conclusions can be drawn as, 1) damage failure evolves with dimension of the specimen, and difference of the fracture energy dissipated per unit is the main reason of the presence of size effect in concrete subjected to bi-axial compression. 2) an obvious size effect can be observed on the uniaxial/biaxial compressive strength of concrete and the simulation results of present work follow closely the size effect law (SEL) proposed by Bažant.