These authors contributed equally to this work. InSb is one of the promising candidates to realize a topological state through proximity induced superconductivity in a material with strong spin-orbit interactions. In two-dimensional systems, thin barriers are needed to allow strong coupling between superconductors and semiconductors. However, it is still challenging to obtain a high-quality InSb two-dimensional electron gas in quantum wells close to the surface. Here we report on a molecular beam epitaxy grown heterostructure of InSb quantum wells with substrate-side Si-doping and ultra-thin InAlSb (5 nm, 25 nm, and 50 nm) barriers to the surface. We demonstrate that the carrier densities in these quantum wells are gate-tunable and electron mobilities up to 350,000 cm 2 (Vs) −1 are extracted from magneto-transport measurements. Furthermore, from temperature-dependent magneto-resistance measurements, we extract an effective mass of 0.02 m 0 and find a Zeeman splitting compatible with the expected band edge g-factor.