On a meso-level, concrete can be seen as a three-phase composite material comprising a cement base, aggregate, and a transitional zone between the cement and aggregate. In this study, based on the random characteristics of the aggregate distribution and morphology, the Walraven formula is applied to determine the convex polygonal aggregate distribution of the two-dimensional concrete specimen's cross-section. Subsequently, an algorithm for the random convex polygon aggregate is proposed, in which an area of round aggregate is used as the control parameter and the inscribed polygon of the round aggregate is used as the framework. A numerical experiment is conducted on specimens under uniaxial compression by using the high-strength and high-performance concrete C80 as an example, and corresponding stress-strain curves and damage evolution pictures are drawn. A comparison between results of the numerical simulation and the physical test show that the numerical model proposed in this paper is both reasonable and feasible.