Graphene with high carrier mobility μ is required both for graphene-based electronic devices and for the investigation of the fundamental properties of Dirac fermions. An attractive approach to increase the mobility is to place graphene in an environment with high static dielectric constant κ that would screen the electric field due to the charged impurities present near graphene's surface. Here we investigate the effect of the dielectric environment of graphene and study electrical transport in multi-terminal graphene devices suspended in liquids with κ ranging from 1.9 to 33. For non-polar liquids (κ<5), we observe a rapid increase of μ(κ), with room-temperature mobility reaching ~60,000 cm2 Vs-1 for devices in anisole (κ=4.3). We associate this trend with dielectric screening of charged impurities adsorbed on graphene. We observe much lower mobility μ~20,000 cm2 Vs-1 for devices in polar liquids (κ≥18) and explain it by additional scattering caused by ions present in such liquids.