From mesoscale aspect, concrete was considered as a three-phase composite material consisting of aggregate, cement mortar and the interfacial transition zone between aggregate and cement mortar. Based on Python language, a unite-cell model with periodicity was established by using Monte Carlo method. The prediction method of equivalent elastic modulus of concrete was proposed by combining homogenization theory and periodic boundary conditions. The predicted values of the model were compared with the results in existing literature to verify the validity of the present model. On this basis, the influences of unite-cell size, interfacial transition zone thickness, aggregate volume rate and maximum aggregate size on the equivalent elastic modulus of concrete were investigated. The results show that the unite-cell model can effectively predict the elastic properties of concrete composite materials. The error locates in the range of 1.87% to 4.97%, compared with the existing results. The size of concrete unite-cell model is recommended to be 150 mm. In the range of 20% to 40%, the aggregate volume rate has significant effect on the equivalent elastic modulus of concrete. Moreover, the interfacial transition zone thickness and maximum size of aggregate exhibit slight effect on the equivalent elastic modulus of concrete, showing a monotonically decreasing or monotonically increasing effect pattern.