In this paper, we present a 3D parallelized test-particle model of Ganymede's neutral environment. The atmosphere sources are assumed to be the sputtering and the sublimation of water-ice, the former taking place in the polar regions and the latter near the subsolar point. It appears that Ganymede's atmosphere is deeply structured by these two processes, leading to a strong dichotomy between polar and subsolar regions. The densest part of the atmosphere is found in the vicinity of the subsolar point, where sublimated H2O is the predominant species near the surface. At higher latitudes and on the nightside, O2 prevails at low altitude, whereas the high altitudes are primarily populated by H2 everywhere in the atmosphere. An estimation of the number of collisions shows that the atmosphere is mostly collisionless, except a small region near the subsolar point. The O2 column density in our model is in good agreement with the observations. However, it appears that we underestimate the H density. This could suggest that the sublimation rates are significantly underestimated but not the sputtering. The escape rates of the different species are essentially lower than those previously obtained by Marconi (2007). The effects of varying surface emission fluxes are investigated in order to simulate Ganymede's passing into the shadow of Jupiter or in the plasma sheet. We estimate that the sublimated H2O peak in the subsolar region would disappear within one hour in the shadow of Jupiter. Likewise, the variation of the sputtering fluxes alters the atmospheric structure in a similar time scale.