In order to reveal the size effect meso-heterogeneity mechanism of concrete strength, the meso-element equivalent heterogeneity model was established. Tension and compression tests were simulated for different size meso-heterogeneity models. The results showed that the size effect of concrete is rooted in the meso-heterogeneity mechanism of materials. With the increase of model size, the variation coefficient of meso-element elastic modulus increases and meso-heterogeneity of concrete heightened. Also, more low-strength units or defects were discovered in the large-size model. As a result, the tension and compression strength of concrete and the ultimate strain decreased and the brittleness of concrete strengthened. Concrete damage region extended from the concentrated area to multiple non-penetrating crack zones.