Utilizing the latest SCAN-rVV10 density functional, we thoroughly assess the electrochemical properties of 35 Mo-based ordered double transition metal MXenes, including clean Mo2MC2 (M = Sc, Ti, V, Zr, Nb, Hf, Ta) and surface functionalized structures Mo2MC2T2 (T = H, O, F and OH), for the potential use as anode materials in lithium ion batteries (LIBs). The first principles molecular dynamics simulations in combination with the calculations of the site adsorption preferences for Li atoms on all investigated MXenes reveal that both Li-saturated adsorption structures and theoretical capacities of Mo-based MXenes are fundamentally influenced by the surface terminations. We find that the adsorption of Li atoms on either -OH or -F functionalized MXenes is chemically unstable. In particular, the F-groups prefer to form a separate fluoride layer with Li atoms, detaching from the Mo2MC2 substrates. The Li atoms could form a stable single adsorption layer on the -H, -O and intrinsic MXenes surface, exhibiting theoretical capacities in the range from 121 mA h g-1 to 195 mA h g-1. Besides -F and -OH terminations, the remaining Mo-based MXenes also possess superior flat open circuit voltage (OCV) profiles with the most reversible storage capacity below 1.0 V during the charging/discharging cycles. We further predict the low barrier heights of Li-ion diffusion, at a range of 0.03-0.06 eV for most Mo-based MXenes except -O and -H terminations, exceeding that of graphene or Ti3C2. Furthermore, combining the Vineyard transition state theory (TST) with the phonon spectra obtained from density functional perturbation theory (DFPT), the mean planar diffusion coefficient is calculated to be 2 × 10-8 m2 s-1 at 300 K for intrinsic Mo2MC2 monolayers. Although the overall specific capacity is fundamentally restricted with the relatively heavy molecular mass of MXenes, we conclude that Mo-based structures, especially the intrinsic Mo2MC2 (M = Sc, Ti, V) monolayers, might be promising anode materials from the aspect of fast charging/discharging application for LIBs.