The importance of the meso-scale analysis of concrete has been a controversial topic. The accuracy and efficiency of numerical modelling directly influence the results and computational cost. In this study, we propose a versatile fractal-geometry-based modelling method that can generate an aggregate model with a known gradation curve. Two numerical meso-model groups generated by the random fractal method are measured and analysed considering the gradation curve, coarse aggregate content, and fractal dimension as evaluation indices. It is verified that the evaluation indices of the numerical models are consistent with the actual ones. Based on sampling statistical analysis, the geometrical homogenization of the meso-model generated by the random fractal method is found to be satisfactory for meso-scale applications. Furthermore, the random fractal method is shown to have low algorithm complexity. (C) 2017 Elsevier B.V. All rights reserved.