Lightweight aggregate concrete (LAC) possesses the merits of low density, excellent thermal insulation performance and outstanding seismic performance. However, the practical application in structural engineering is limited because its mechanical properties are weaker than those of ordinary aggregate concrete. It was found that the compressive strength of high-strength concrete prepared by autoclaved silicate lightweight aggregate (cloud concrete stone) was higher than that of ordinary aggregate high-strength concrete, and it showed significant lightweight and high-strength characteristics. To reveal the enhancing mechanism of the mechanical properties of high-strength concrete prepared by cloud concrete stone (CCS), this research examines the internal curing effect of CCS and the mechanical performances of the interfacial transition zones (ITZ). The influences of the elastic modulus of CCS, the shape of aggregate and fracture patterns on the mechanical properties of concrete are simulated via the discrete element method. The findings suggest that the internal curing effect of CCS delays the onset of capillary stress and mitigates autogenous shrinkage. The homogeneousness, elastic modulus, and fracture toughness of ITZ around CCS aggregate are superior than that ITZ around ordinary gravel in high-strength concrete. Furthermore, the small difference in elastic modulus between CCS aggregate and cement matrix is advantageous for preventing microcracks during compression tests. The round shape of the aggregate also mitigates the development of microcracks caused by the stress concentration effect. These three reasons contribute to the enhancement of mechanical properties in lightweight and high-strength concrete. The innovation of this research is that the intrinsic relationship between CCS aggregate and concrete’s mechanical properties is thoroughly revealed from the aspects of the characteristics of the interface transition zone, the morphology of the aggregate and the elastic modulus of aggregate. That provides a theoretical basis for the application of light aggregate in high-strength structural concrete.