Many experiments have shown that carbon nanotube-coated (CNT-coated) graphene foam (CCGF) has specific mechanical properties, which further expand the application of graphene foam materials in many advanced fields. To reveal the microscopic deformation mechanism of CCGF under uniaxial compression and the main factors affecting their mechanical properties, numerical experiments based on the coarse-grained molecular dynamics method are systematically carried out in this paper. It is found that the relative stiffness of CNTs and graphene flakes seriously affects the microscopic deformation mechanism and strain distribution in CCGFs. The bar reinforcing mechanism will dominate the microstructural deformation in CCGFs composed of relatively soft graphene flakes, while the microstructural deformation in those composed of stiff graphene flakes will be dominated by the mechanical locking mechanism. The effects of CNT fraction, distribution of CNTs on graphene flakes, the thickness of graphene flakes, and the adhesion strength between CNTs and graphene flakes on the initial and intermediate moduli of foam materials are further studied in detail. The results of this paper should be helpful for a deep understanding of the mechanical properties of CCGF materials and the optimization design of microstructures in advanced graphene-based composites.