Identifying applicable anode materials is a significant task for Li-and Na-ion battery (LIB and NIB) technologies. We propose the GaN monolayer (2D GaN) can be a good anode candidate. The GaN monolayer manifests stable Li/Na adsorption and inherently low theoretical voltages. Most excitingly, both high storage capacity and extremely fast Li/Na diffusion can be simultaneously realized in the GaN monolayer. For Li, the storage capacity and diffusion barrier is 938 mA h g -1 and 80 meV , respectively.And the values for Na are 625 mA h g -1 and 22 meV. Comparing with known 2D anode materials with similar scale of ion diffusion barriers, the GaN monolayer almost possesses the highest Li/Na storage capacity discovered to date. Our work suggests that the 2D GaN is a prospective anode material offering fast ion diffusion and high storage capacity.The Li-ion batteries (LIBs) have been intensively used nowadays. The success of LIBs mainly benefits from their excellent energy conversion efficiency and good storage capacity. 1-5 Nevertheless, the development of LIBs has currently faced increasing challenge due to the naturally limited lithium resource and their high production cost. [6][7][8] As a result, non-Li-ion batteries have emerged in recent years. 9-15 Among them, Na-ion batteries (NIBs) have attracted the most attentions. 9,10 This arises from that the sodium has relatively low cost. For LIBs and NIBs, the electrochemical performance is the most dependent on their electrode materials; thus developing good electrode materials is one of major focuses in current battery technologies. Two-dimensional (2D) materials have offered great potential as ion battery electrodes, because their fully exposed surfaces are believed to provide fast ion diffusion and the maximum ion insertion channels. [16][17][18] Up to date, several families of 2D materials, such as graphene, [19][20][21] MXenes, [22][23][24][25][26][27][28] transition-metal dichalcogenides (TMDCs), 29-32 transition-metal dinitrides (TMDNs), 33 borophenes, 34-36 and others [37][38][39][40] have been identified as LIBs and NIBs electrodes. For battery electrode materials, the ion diffusion speed and the storage capacity are two of the most crucial indicators for the electrode performances. However, most known 2D electrode materials can only achieve high performance on one of these indicators. 2D anode materials, for example, Mo 2 C, 24,25 Nb 2 C 26 and Ti 3 C 2 23 are proposed to offer very fast Li/Na diffusion speed but have low or moderate storage capacities; silicence 41 and β 12 /χ 3 Borophene 35 show extremely high Li/Na storage capacities but have poor ion diffusion speed. Thus there is urgent need to explore excellent electrode materials which can offer fast ion diffusion and high storage capacity simultaneously.As a well-known semiconductor, GaN has been widely used for variable applications. 42 Unlike traditional 2D materials, it is previously quite a challenge to prepare freestanding 2D GaN by routine exfoliation technologies, because its bulk phase natural...