Red supergiant stars represent a late stage of the evolution of stars more massive than about nine solar masses, in which they develop complex, multi-component atmospheres. Bright spots have been detected in the atmosphere of red supergiants using interferometric imaging. Above the photosphere of a red supergiant, the molecular outer atmosphere extends up to about two stellar radii. Furthermore, the hot chromosphere (5,000 to 8,000 kelvin) and cool gas (less than 3,500 kelvin) of a red supergiant coexist at about three stellar radii. The dynamics of such complex atmospheres has been probed by ultraviolet and optical spectroscopy. The most direct approach, however, is to measure the velocity of gas at each position over the image of stars as in observations of the Sun. Here we report the mapping of the velocity field over the surface and atmosphere of the nearby red supergiant Antares. The two-dimensional velocity field map obtained from our near-infrared spectro-interferometric imaging reveals vigorous upwelling and downdrafting motions of several huge gas clumps at velocities ranging from about -20 to +20 kilometres per second in the atmosphere, which extends out to about 1.7 stellar radii. Convection alone cannot explain the observed turbulent motions and atmospheric extension, suggesting that an unidentified process is operating in the extended atmosphere.