Owing to their cost-effectiveness and the natural abundance of magnesium, magnesium-ion batteries (MIBs) were introduced as encouraging alternatives to Lithium-ion batteries. Following the successful synthesis of carbon nano-tube, its B and N doped derivatives which were doped with B and N enjoyed the attention of researchers as novel anode materials (AM) for MIBs. Here, we investigated a BC2N nano-tube (BC2NNT) as an encouraging AM for MIBs. To have a deeper understanding of the electrochemical properties, cycling stability, specific capacity (SC) and the adsorption behavior of this nano-tube, first-principles density functional theory computations were performed. By performing NMR calculations, we identified two types of non-aromatic hexagonal rings, namely B2C2N2 (I) and BC4N (II). Magnesium was adsorbed onto I with the adsorption energy of −40.38 kcal/mol and on II with the adsorption energy −20.15 kcal/mol. The SCs were as high as 783 mAh/g. The predicted average open-circuit voltage for BC2NNT was 1.94 V, which was greater than that of other 2D materials. The findings demonstrated the possibility of utilizing the BC2NNT as an AM for MIBs. The results can provide useful insights into the design of boron-carbon-nitrogen-based AMs for MIBs.