The recent observation of the superconducting state at atomic scale has motivated the pursuit of exotic condensed phases in two-dimensional (2D) systems. Here we report on a superconducting phase in two-monolayer crystalline Ga films epitaxially grown on wide-band-gap semiconductor GaN(0001). This phase exhibits a hexagonal structure and only 0.552 nm in thickness, nevertheless, brings about a superconducting transition temperature Tc as high as 5.4 K, confirmed by in situ scanning tunneling spectroscopy and ex situ electrical magnetotransport and magnetization measurements. The anisotropy of critical magnetic field and Berezinski-Kosterlitz-Thouless-like transition are observed, typical for the 2D superconductivity. Our results demonstrate a novel platform for exploring atomic-scale 2D superconductors, with great potential for understanding the interface superconductivity.