We have investigated channel thickness (L-w) dependence of transport properties of two-dimensional-electron gas (2DEG) in pseudomorphic In(0.74)G(0.26)As/In0.52Al0.48As quantum well high electron mobility transistor (QW-HEMT) structures with extremely flat heterointerfaces [(4 1 1)A super-flat interfaces] grown on (4 1 1)A InP substrates by molecular beam epitaxy (MBE). The highest electron mobility of 90,500 cm(2)/V s (77 K) with a sheet carrier concentration (N-s) of 3.1 x 10(12) cm(-2) was observed for the (4 1 1)A QW-HEMT structure with L-w = 8 nm, which is about 1.5 times larger than the best value (mu = 61,000 cm(2)/V s at 77 K) of ever reported electron mobility with a similar N-s of 3.0 x 10(12) cm(-2) for the InGaAs/InAlAs QW-HEMT structure grown on a (1 0 0) InP substrate. This enhancement of the electron mobility of the (4 1 1)A QW-HEMT structure is mainly due to much improved flatness of the (4 1 1)A InGaAs/InAlAs heterointerfaces compared with those of conventional (1 0 0) interfaces, which results in a large reduction of interface roughness scattering of 2DEG.