A two-dimensional (2D) transition metal carbonitride (MXenes) with a formula of Ti3CN as an anode of a lithium-ion battery (LIB) has been proposed in this work. The mechanism of Li+ adsorption and diffusion on the surface of Ti3CN and Ti3CNT2 (T = F, O, and OH functional groups) was studied to estimate the potential application of Ti3CN as an anode material by density functional theory (DFT) and DFT+U computations. For Ti3CNT2 (T = O, F, OH), the value of Li diffusion barriers is from 0.2 eV to 0.3 eV. On the basis of our results, we can know that Li prefers adsorption on the nitrogen side for Ti3CN in the absence of functional groups and tends to adsorb on the carbon side for Ti3CNT2 (T = O, F, OH). This phenomenon can be explained by Bader charge population analysis. For Ti3CNF2, Li-F formed a six-membered ring with increasing Li concentration, thereby making the system more stable. This work contributes to offering perspectives for carbonitride systems (MXenes) as LIB anodes.