The global density distribution of atomic H in the upper atmosphere of Venus is determined in terms of a global circulation model. It is shown that H produced on the dayside is efficiently advected to the nightside by the major gas CO2 where it is then convected to lower altitudes and recombines. A maximum night/day H density ratio of about 5 is derived, in which case exospheric return flow from night to day strongly limits the nightside density enhancement. A previously postulated onstraint connecting the eddy diffusion coefffieient with the escape flux of H in one dimensional models is no longer required when global circulation of H is considered.