Rechargeable lithium-ion batteries as the main energy storage equipment should possess high power density, excellent reversible capacity, and long cycle life. However, due to the high cost and dendrites growth of Li, searching for non-Li-ion batteries is urgent. Compared to lithium, magnesium has abundant resources, smaller ionic radius, and high energy density. Therefore, magnesium-ion batteries (MIBs) can act as the next generation metal-ion batteries. Two-dimensional materials based on Be or B element acting as the anode of metal-ion batteries always exhibit high theoretical storage capacity. Using first-principles calculations, we systematically explore the potential of BeB₂ as MIBs anode. The optimized BeB₂ monolayer structure shown in Fig. 1a consists of two atomic layers, where each Be atom is coordinated with six B atoms, and each B atom is coordinated with three Be atoms. The lattice constants are a = b = 3.037 Å with a thickness of 0.554 Å. From the phonon spectrum calculations, the absence of imaginary modes indicates the dynamic stability of BeB₂ monolayer. The presence of a Dirac cone further suggests the excellent conductivity (Fig. 1b). Three stable adsorption sites (Be₁: Top of Be atoms. Be₂ and B₂: Bottom of Be and B atoms) are labeled in the Fig. 1a. Taking symmetry into account, we consider three pathways to evaluate the migration of Mg atom on BeB₂ monolayer (Fig. 1c). The corresponding lowest diffusion energy barrier is 0.04 eV along Path III. The stable configuration with the maximum adsorption Mg concentration is shown in Fig. 1d, which generates a theoretical capacity of 5696 mAhg^-1. The calculated average open-circuit voltage is 0.33V. Based on ab initio molecular dynamics simulations, the total energy of BeB₂ with Mg adsorbed fluctuates within a narrow range, suggesting that BeB₂ can sustain structural stability after the storage of Mg at room temperature (Fig.1e). Finally, for practical application, we investigate the adsorption and diffusion behavior of Mg on bilayer BeB₂. Three configurations are considered: AA stacking (overlapping of Be atoms in upper layer with Be atoms in lower layer), AB stacking (overlapping of Be atoms in upper layer with B atoms in lower layer), and AC stacking (overlapping of Be atoms in upper layer with B-B bonds in lower layer). The most stable configuration is AB stacking (shown in Fig. 1f) with the interlayer space of 3.12 Å and the binding energies of -120.97 meV/atom. Compared to the BeB₂ monolayer structure, the adsorption energy of Mg is -2.24 eV for Be₁, -1.38 eV for B₅ site, and -1.90 eV for B₄ site, while the lowest diffusion energy barrier is 0.13 eV along the path of B₅-Be₃-B₅. Therefore, based on the above-mentioned properties, we believe BeB₂ monolayer can act as an excellent MIBs anode material.