The rational design of high-performance anode materials is crucial for the development of rechargeable Na-ion batteries (NIBs) and K-ion batteries (KIBs). In this study, based on density functional theory (DFT) calculations, we have systematically investigated the possibility of a bilayer triazine-based covalent organic framework (bilayer TCOF) as an anode for NIBs and KIBs. The calculation of the electronic band structure shows that the bilayer TCOF is a direct band gap semiconductor with a band gap of 2.01 eV. After the adsorption of Na/K at the most favorable sites, the bilayer TCOF transitions from a semiconductor to a metal state, guaranteeing good electronic conductivity. The low diffusion barriers of the bilayer TCOF are 0.45 and 0.26 eV, respectively, indicating a fast diffusion rate of Na/K ions. In addition, the bilayer TCOF has a theoretical storage capacity of up to 628 mA h g-1. Finally, it is found that the average voltage of the bilayer TCOF for NIBs and KIBs is 0.53 and 0.48 V, respectively. Based on these results, we can conclude that the bilayer TCOF may be a suitable anode material for NIBs and KIBs.