We explore the feasibility of inverting freely available altimetry-derived gravity grids for sediment thickness on oceanic crust. A four-layer Earth model is adopted, assuming that the gravity signal from the base of the sedimentary layer can be fully isolated from the observed free-air gravity. The following additional data are required: (1) shipboard bathymetry for reliable Bouguer correction, (2) oceanic crustal ages to correct for gravity anomalies related to the thermal history of lithospheric breakup and seafloor spreading, and (3) some wide-angle seismic observations of sediment thickness. A fixed relationship between the base of the sedimentary layer and the Moho is also required because of limited gravity resolution at large depths. The final inversion setup searches for three control parameter values (density of uppermost sediments, density of oceanic crystalline crust, and thermal diffusivity of mantle rock) that minimize misfit between the Earth model and observations. Applied to the Norwegian--Greenland Sea, the inversion successfully predicts locations of >20--25 km wide depocenters and crystalline crustal highs, yet ~1 km thickness errors are common even in well-constrained areas. The largest errors are associated with underplated crust, active mid-ocean ridges, and the continent-ocean boundary, indicating locally incorrect assumptions of mantle thermal structure and crystalline crustal thickness. The thicknesses of >4 km thick submarine fans are underpredicted, probably because of too low sedimentary densities in the Earth model. If these limitations are acceptable or do not apply because of simple crustal structure, gravity inversion may be used for mapping regional sedimentary patterns, e.g., in the Arctic Ocean.