The superconducting behaviour of InN has been observed in many experiments where the origin of superconductivity is addressed to presence of (i) In-In chains in ab-plane, (ii) specific carrier density range limited Mott transition critical carrier density and (iii) presence of In O-2(3) impurities. Although the superconductivity can be observed when the above conditions are enough for epitaxial grown InN films, the superconductivity properties of InN, so far, have not worked comprehensively. Here, we report the magneto-resistance, upper critical field and thermally activated flux mechanism of superconductor Mg doped InN epitaxial film grown by Molecular Beam Epitaxy. The superconducting phase transition temperature was observed at similar to 3.9 K at zero magnetic field. The carrier density of the film is found in the range of Mott transition and superconductivity to metal transition. The effect of magnetic field on the superconductivity of Mg-doped InN film is studied by employing the magnetoresistance and Hall resistance measurement with a typical Hall-bar shape device. The magnetoresistance analysis has been carried out by flux-flow and flux-creep models. The activation energy is found as highly sensitive with field in a range of 0.0 to 1.0 T. The upper critical field at zero temperature and coherence length estimated by Ginzburg-Landau relation were found as around 0.8 T and 216.9 angstrom, respectively. The superconducting properties of the epitaxial growth Mg-doped InN film are discussed through the manuscript.