Ganymede's surface exhibits great geological diversity, with old dark terrains, expressed through the surface composition, which is known to be dominated by two constituents: H2O-ice and an unidentified darkening agent. In this paper, new investigations of the composition of Ganymede's surface at global scale are presented. The analyses are derived from the linear spectral modeling of a high spectral resolution dataset, acquired with the near-infrared (1.40–2.50 μm) ground-based integral field spectrometer SINFONI (SINgle Faint Object Near-IR Investigation) of the Very Large Telescope (VLT hereafter) located in Chile. We show that, unlike the neighboring moon Europa, photometric corrections cannot be performed using a simple Lambertian model. However, we find that the Oren-Nayar (1994) model, generalizing the Lambert's law for rough surfaces, produces excellent results. Spectral modeling confirms that Ganymede's surface composition is dominated by H2O-ice, which is predominantly crystalline, as well as a darkening agent, but it also clearly highlights the necessity of secondary species to better fit the measurements: sulfuric acid hydrate and salts, likely sulfates and chlorinated. A latitudinal gradient and a hemispherical dichotomy are the strongest spatial patterns observed for the darkening agent, the H2O-ice, and the sulfuric acid: the darkening agent is by far the major compound at the equator and mid-latitudes (≤ ± 35°N), especially on the trailing hemisphere, while the H2O-ice and the sulfuric acid are mostly located at high latitudes and on the leading hemisphere. This anti-correlation is likely a consequence of the bombardment of the constituents in the Jovian magnetosphere which are much more intense at latitudes higher than ±35°N. Furthermore, the modeling confirms that polar caps are enriched in small, fresh, H2O-ice grains (i.e. ≤50 μm) while equatorial regions are mostly composed of larger grains (i.e. ≥200 μm, up to 1 mm). Finally, the spatial distribution of the salts is neither related to the Jovian magnetospheric bombardment nor the craters. These species are mostly detected on bright grooved terrains surrounding darker areas. Endogenous processes, such as freezing of upwelling fluids going through the ice shell, may explain this distribution. In addition, a small spectral residue that might be related to brines and/or hydrated silica-bearing minerals are located in the same areas.