With the rapid development of electric vehicles and portable electronic devices, high-performance energy storage devices such as Na-ion batteries (NIBs) have received increasing attention. Here, the possibility of two-dimensional (2D) zirconium-nitrogen compounds as anode materials for Na-ion batteries has been discussed by first-principles calculations. The results show that t-Zr2N is the most stable compared with other structures (ZrN, h-Zr2N, t-ZrN2, h-ZrN2, and p-ZrN2). On this basis, the most stable adsorption structures of t-Zr2N with various functional groups (-O, -OH, -F) were established, and their performance as NIBs anode materials was evaluated. We found that sodium (Na) ions were not easily adsorbed on Zr2NF2 and therefore were not suitable as electrode materials, while the other three structures (Zr2N, Zr2NO2, and Zr2N(OH)2) were all metallic and had a good performance as anode materials. Zr2N is the most suitable anode material owes to its high theoretical capacity (545.9 mAhg-1), extremely low diffusion barrier (0.018 eV), good stability and suitable open-circuit voltage, which makes its application in battery with great potential. Meanwhile, our investigations found that functional groups will affect the performance of 2D materials as electrode materials, which can provide useful guidance for future relevant researches.