Searching for high-performance anode materials with high energy-density, fast kinetics, and good stability is a key challenge for non-lithium-ion batteries (NLIBs), such as Na+, K+, Mg2+, Ca2+, Zn2+ and Al3+ ion batteries. Here, we systematically investigated the performance of a new class of two-dimensional tetragonal transition-metal carbides (tetr-MCs) using first-principles calculations, as anodes for NLIBs. The results show that tetr-MCs are ideal anode materials with good stabilities, favorable mechanical properties, intrinsic metallic properties, high theoretical capacities, and fast ion diffusion rate for NLIBs. Among all tetr-MCs, we found that the energy barrier of Mg atoms on tetr-TiC is only 54 meV and that of Al atoms on tetr-VC is 101 meV, which are lower than the energy barriers of 230-500 meV of the well-studied MXenes, indicating that tetr-VC and tetr-TiC monolayers are promising anodes for NLIBs. Therefore, compared to MXenes, tetr-MCs show many advantages for NLIB applications, such as a lower diffusion barrier (minimum 54 meV), a high theoretical capacity (up to 1450 mA h g-1), and a lower average open circuit voltage (0.05-0.77 V). The results are of great significance for the experimental preparation of excellent anode materials for NLIBs.