The weak visible-infrared broadband electromagnetic absorption, absence of bandgap, and low out-of-plane Young's modulus in graphene are three long-standing challenges plaguing its applications in optoelectronic and photonic devices. Herein, we propose a novel atomic-scale graphene metamaterial via vertically crossing graphene nanosheets, showing remarkable energetical, dynamical, and mechanical stability from state-of-the-art theoretical calculations. Compared with the zero bandgaps in pristine graphene, our graphene metamaterial exhibits a gap of 107 meV. Using pressure engineering, a tunable bandgap in the range of 0–260 meV was obtained, enabling our graphene metamaterial huge potential in semiconductor-based modern electronic devices. Anisotropic Young's moduli of over 1 TPa along the  direction and 413 GPa along the  direction were demonstrated. The in-plane Young's modulus (1085 GPa) is higher than that of the state-of-the-art technical ceramics such as SiC (about 425 GPa), Al2O3 (about 400 GPa), and Si3N4 (about 300 GPa), and the out-of-plane Young's modulus (413 GPa) is significantly increased comparing with monolayer graphene (about 2 GPa). Significant enhancement of broadband electromagnetic absorption for the visible (400–800 nm) and infrared light (1–6 μm) was achieved with a value of 50–1000 times higher than that of monolayer graphene, which promises the present graphene metamaterial a potential building block for photonic and optoelectronic devices.