AlGaAs/GaAs two-dimensional electron gases (2DEGs) are grown on GaAs substrates by molecular beam epitaxy (MBE) with various thicknesses of GaAs buffer layers. Prior to the growth, the substrates are cleaned using an electron cyclotron resonance (ECR) hydrogen plasma at low temperatures where native oxides are not removed from the surface by heating alone. The electrical properties of 2DEGs are evaluated using van der Pauw and Hall effect measurements. The sheet carrier densities and electron mobilities of the plasma-cleaned samples with more than 20-nm-thick buffer layers exhibit almost the same properties as the sample with a 600-nm-thick buffer layer at 77 K. ECR hydrogen plasma cleaning is found to be a promising technique for the regrowth process.