The structure of an alpha-Mo2C(0001) surface varies depending on the annealing temperature. At least three phases are observed by low energy electron diffraction (LEED). A well-ordered (root 3 x root 3)R30 degrees structure was observed on alpha-Mo2C(0001) at annealing temperatures below 960 K, which was imaged as a honeycomb structure by scanning tunneling microscopy (STM). A model was proposed for the C-terminated structure where C atoms are located on the threefold hollow sites of a Mo layer, and each carbon atom is observed as a depression of the honeycomb structure by STM. An increase in carbon coverage on the surface transformed the (root 3 x root 3)R30 degrees structure to a c(2x4) structure where zigzag rows running parallel tb each other were observed by STM.