Recently "carbon ene-yne" (CEY), a novel full carbon two-dimensional (2D) material was successfully synthesized by the solvent-phase reaction. Motivated by this experimental effort, we conducted extensive first-principles density functional theory simulations to explore the application prospects of CEY as an anode material for Mg, Na and Li-ion batteries. To simulate the ionic intercalation process in an anode electrode, the adatoms coverage was gradually increased. We then employed Bader charge analysis to evaluate the charge transfer between the adatoms and the CEY nanosheet and finally to report the theoretical storage capacity of the anode. We particularly studied the evolution of adsorption energy, electronic density of states and open-circuit voltage with respect to adatoms coverage. The diffusion of an adatom over the CEY surface was also investigated by using the nudged elastic band method. Remarkably, our results suggest CEY as a promising anode material containing the highest theoretical charge capacities among 2D materials studied so far, with ultrahigh capacities of 2,680 mAh/g and 1,788 mAh/g for Li and Na-ion batteries, respectively. The provided insight by this study 2 highlights the CEY as a novel full carbon material with properties, highly desirable for the application as anode material in the next generation rechargeable ion batteries.