We report on the liquid-phase epitaxial growth of the single-crystalline Bi2Sr2CaCu2Ox (Bi-2212) films. As in the case of the travelling solvent floating zone method, the Bi-2212 films are grown from a liquid phase by sweeping a heating zone. A specific point is that the liquid phase takes the form of a two-dimensional layer between two MgO substrates, which yields the excellent epitaxial growth. The films display a multigrain structure, and the maximum grain size is typically 1 mm in the in-plane directions and a few microns in thickness. The zero resistance state is attained at 86 K. From the x-ray rocking curves of the films and substrates, we infer that the mosaic structures in substrates degrade the crystallinity of the films. In the x-ray pole figure experiment we observe the misorientation angle of 12° between Bi-2212 [100] and MgO [100] directions as a major epitaxial state.