We report on the superconducting characteristics of the Indium thin films on molybdenum under-layer as a function of the In film thickness. Our molybdenum under-layer with thickness of 50 ร
does not cause the occurrence of superconductivity until 1.5 K and the sheet resistance has logarithmic temperature dependence observed in the present investigation. As thickness of In increased, the oscillation phenomenon of T C was observed at early stage of deposition and the value of T C is higher than the that for bulk of In. Furthermore, it is found that with increase of the In thickness, there are large differences of the strengths of the upper critical magnetic field H C2 (T), resistivity and T C between films with thickness below and above 100 ร
. On the other hand, the T C decreases monotonously as sheet resistance increases, when the T C is plotted against sheet resistance. To clarify the relation of superconducting characteristics and the surface structure of the films with different thickness, we have performed surface observation by atomic force microscope. As a result, we have found that the surface changes from homogeneous structure to inhomogeneous (or percolative) structure, when the thickness of in films pass through about 100 ร
. Superconductivity of In/Mo films with relatively thick-inhomogeneous films cannot be explained in terms of the simple percolation theory. Therefore, we analysis the experimental data of H C2 (T) near T C , using a extended Landau-Ginzburg model. It is found out that our In/Mo films must consider some factors; such as, grain size, the distance of grain space, and the strength of couplings between grains.