Abstract: Two-dimensional MXenes continue to receive much research attention owing to their versatility and predicted topological phase, which are yet to be fully explored. Here, we conduct a rigorous search on ${M}_{2}^{\ensuremath{'}}{M}^{\ensuremath{''}}{\mathrm{C}}_{2}$ $({M}^{\ensuremath{'}}=\mathrm{V}, \mathrm{Nb}, \mathrm{or} \mathrm{Ta};{M}^{\ensuremath{''}}=\mathrm{Ti}, \mathrm{Zr}, \mathrm{or} \mathrm{Hf})$ with various surface terminations, ${X}_{2}$ $(X=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}, \mathrm{O}, \mathrm{H}, \mathrm{or} \mathrm{OH})$, using first-principles calculations. The majority of the systems exhibit the topological phase with semimetallic band structures. Most importantly, fluorinated MXenes, ${M}_{2}^{\ensuremath{'}}{M}^{\ensuremath{''}}{\mathrm{C}}_{2}{\mathrm{F}}_{2}$, are topological insulators. They possess sizable nontrivial band gaps from 34 to 318 meV using Heyd-Scuseria-Ernzerhof (HSE) hybrid functional calculations which are within the range capable of realizing quantum spin-Hall effects even at room temperature. Furthermore, the $d$ orbitals of ${M}^{\ensuremath{'}}$ and ${M}^{\ensuremath{''}}$ atoms mostly contribute to the spin-orbit coupling-induced band gaps. Selecting ${\mathrm{V}}_{2}\mathrm{Ti}{\mathrm{C}}_{2}{\mathrm{F}}_{2}$ as an exemplar, we demonstrate the presence of edge states, verifying the calculated ${Z}_{2}$ invariant, and reveal its robustness against tensile strain. Finally, we propose SiC(0001) as a candidate substrate for material realization as it can preserve the nontrivial band topology.