The processes leading to the birth of low-mass stars such as our Sun have been well studied, but the formation of high-mass (over eight times the Sun's mass, M(o)) stars remains poorly understood. Recent studies suggest that high-mass stars may form through accretion of material from a circumstellar disk, in essentially the same way as low-mass stars form, rather than through the merging of several low-mass stars. There is as yet, however, no conclusive evidence. Here we report the presence of a flattened disk-like structure around a massive 15M(o) protostar in the Cepheus A region, based on observations of continuum emission from the dust and line emission from the molecular gas. The disk has a radius of about 330 astronomical units (Au) and a mass of 1 to 8 M(o). It is oriented perpendicular to, and spatially coincident with, the central embedded powerful bipolar radio jet, just as is the case with low-mass stars, from which we conclude that high-mass stars can form through accretion.