Planets with high obliquity receive more radiation in the polar regions than at low latitudes, and thus, assuming an ocean-covered surface with sufficiently high heat capacity, their meridional temperature gradient was shown to be reversed for the entire year. The objective of this work is to investigate the drastically different general circulation of such planets, with an emphasis on the tropical Hadley circulation and the mid-latitude baroclinic eddy structure. We use a 3D dry dynamic core model, accompanied by an eddy-free configuration and a generalized 2D Eady model. When the meridional temperature gradient $T_y$ is reversed, the Hadley cell remains in the same direction, because the surface wind pattern and hence the associated meridional Ekman transport are not changed, as required by the baroclinic eddy momentum transport. The Hadley cell under reversed $T_y$ also becomes much shallower and weaker, even when the magnitude of the gradient is the same as in the normal case. The shallowness is due to the bottom-heavy structure of the baroclinic eddies in the reverse case, and the weakness is due to the weak wave activity. We propose a new mechanism to explain the mid-latitude eddy structure for both cases, and verify it using the generalized Eady model. With seasonal variations included, the annual mean circulation resembles that under perpetual annual mean setup. Approaching the solstices, a strong cross-equator Hadley cell forms in both cases, and about 2/3 of the Hadley circulation is driven by eddies, as shown by eddy-free simulations and using a decomposition of the Hadley cell.