Two-dimensional (2D) growth of ultra-thin Sn films is a prerequisite for examining exotic quantum phenomena as one of their crystallized forms is a promising candidate for topological materials. In this study, we have investigated the ultra-thin film growth of Sn at room temperature with a Fe buffer layer on an insulating Al2O3 substrate using molecular-beam epitaxy. By the insertion of a 2- or 4-nm-thick Fe layer, the growth mode of Sn thin films varies from a three-dimensional (3D) island-based mode on Al2O3 to a 2D layer-based mode on Fe. However, the 3D growth mode reappeared when the thickness of Sn (dSn) reached the critical value dcSn of about 1.0 nm, corresponding to three atomic layers. A systematic increase in the sheet conductance with increasing dSn on the Fe buffer layer revealed that the sheet conductance of the Sn film can be characterized for a thickness less than dcSn. The saturation of the sheet conductance above dcSn indicates a disconnection of the Sn film grown by the island-based growth mode. In addition, the reduction in anomalous Hall resistance in the Sn/Fe bilayer with increasing dSn is attributed to the shunting and short-circuit effects of the conductive ultra-thin 2D Sn layer. By considering the strong coupling between Sn and Fe providing large anomalous Hall effects in the bilayer, further optimization of the 2D growth of ultra-thin Sn on Fe will pave the way to investigate exotic interfacial physical phenomena through electrical transport measurement.