Using the warm electron coefficient, the electron mobility, &mgr;inel, limited only by inelastic scattering was studied for two‐dimensional electron gas confined to the GaAs side of an N‐AlGaAs/GaAs heterojunction. The warm electron coefficient &bgr; was measured to be 0.1–3×10−3cm2/V2at the temperature 4.2–30 K. The electron mobility &mgr;inelis interpreted as the upper limit obtained in the condition free of ionized impurity scattering. The relation between &bgr; and electron mobility &mgr;inelfor two‐dimensional electron gas is obtained as &bgr;∝&mgr;inel, when ionized impurity scattering is predominant. Combining the theoretical relations and experimental results, the electron mobility limit of a two‐dimensional electron gas at 4.2 K is found to be about 9.0×106cm2/V sec at sheet electron concentration of 8×1010cm−2. The exponent of its temperature dependence is −1.28.