The quantum spin Hall (QSH) phase is a peculiar physical phenomenon characterized by topologically protected helical edge states,} with potential applications in lower-power electronics and spintronics. Here{,} using first-principles calculations{,} we predict the QSH phase in Mo2M2C3O2 (M = Ti{,} Zr{,} or Hf){,} new members with ordered structures in the family of two-dimensional transition metal carbides (MXenes). The QSH phase which is confirmed by the nontrivial Z2 topological invariant and Dirac edge states arises from a d-d band inversion between the M-dxy{,}x2-y2 and the Mo-dz2 orbitals and a spin-orbital coupling (SOC)-induced splitting of the M-dxy{,}x2-y2 orbital at the [Gamma] point. With different M atoms{, the QSH gap of Mo2M2C3O2 ranges from 38 to 152 meV. These findings will broaden the scientific and technological impacts of both QSH materials and MXenes.