In-plane anisotropic transport, including the anisotropies of mobility (μ e ) as well as of Rashba spin–orbit (SO) coupling constant (α) in inverted In 0.75 Ga 0.25 As/In 0.75 Al 0.25 As hetero-junction two-dimensional electron gas (2DEG) are observed and discussed. As large as 30% difference between the mobilities, μ e [1¯10] and μ e [110], was confirmed and up to 10% anisotropy of α was likely observed. Since there remains almost no strain at the 2DEG interface, the mobility anisotropy may be attributed to the anisotropies of undulation period of surface morphology and of mosaicity, the direct measure of the threading dislocation density. The anisotropy observed in α is, however, not acceptable because the parameter is determined from the isotropic 2DEG densities estimated from magneto-resistance (MR) measurements. So that, the accuracy of the analysis adopted for determining α is pointed out and the necessity of alternative analysis method is suggested.