Endohedral cluster compounds are a rich source of new superconductors, where nontrivial properties are expected, including strong coupling regime and multigap superconductivity. Here, we report on the synthesis, crystal and electronic structure, and physical properties of the Mo6Ga31 endohedral cluster superconductor. The compound has two crystallographic modifications, monoclinic and triclinic, which are built by the Mo@Ga-10 endohedral clusters. Both structures possess qualitatively the same electronic density of states showing a high peak at the Fermi level. Due to the proximity effect of the triclinic and monoclinic domains, which are in the strong contact with each other, bulk Mo6Ga31 exhibits single superconducting transition at the critical temperature of 8.2 K in zero magnetic field. The upper critical field, which is 7.8 T at zero temperature, shows clear enhancement with respect to the WerthamerHelfand-Honenberg prediction. Accordingly, heat capacity measurements indicate strong electron-phonon coupling in the superconducting state with the large ratio of 2 Delta(0)/(k(B)T(c)) = 4.5, where 2 Delta(0) = 3.2 meV is the full superconducting gap at zero temperature.