Density functional theory (DFT) calculations were employed to probe the feasibility of 2D α-CM (M = N, P) as an anode material for Li-ion batteries (LIBs). Our findings demonstrate the dynamical, mechanical and thermal stability of 2D α-CM. In particular, for the 2D α-CP adsorbed with Li atom, binding energy (E_B) of −2.00 eV ensures favourable adsorption. In contrast to 2D α-CP, the E_B of adsorbed Li atom over α-CN is lower than the cohesive energy of lithium metal, this eliminates the accessibility of 2D α-CN as an anode in LIBs. The Li atom adsorption changes the nature of the 2D α-CP from semiconducting to metallic, ensuring high electronic conductivity. Both partial density of states and L$\ddot{\mathrm{o}}$wdin charge analysis indicate substantial charge transfer from Li atom to 2D α-CP after adsorption. The multilayer adsorption on both sides of 2D α-CP yields Li_5.0CP monolayer with remarkably high specific storage capacity (1108.91 mAhg⁻¹). The obtained average open circuit voltage is suitable for extensive battery application. Diffusion barrier of 0.11 eV shows ultrahigh ionic mobility over the 2D α-CP and thus facilitates charging/discharging process. As a result, high specific storage capacity, lower diffusion barrier, negligible volume change and excellent electronic conductivity imply the promising utility of 2D α-CP as anodic material in LIBs.