We use 3D simulations to study the atmospheric circulation on the first Earth-sized exoplanet discovered in the habitable zone of an M star. We treat Gliese 581g as a scaled-up version of Earth by considering increased values for the exoplanetary radius and surface gravity, while retaining terrestrial values for parameters which are unconstrained by current observations. We examine the long-term, global temperature and wind maps near the surface of the exoplanet – the climate. The specific locations for habitability on Gliese 581g depend on whether the exoplanet is tidally locked and how fast radiative cooling occurs on a global scale. Independent of whether the existence of Gliese 581g is confirmed, our study highlights the use of general circulation models to quantify the atmospheric circulation on potentially habitable, Earth-sized exoplanets, which will be the prime targets of exoplanet discovery and characterization campaigns in the next decade.