This paper investigated the magnetotransport properties of the two-dimensional electron system in an asymmetrical In_0.53Ga_0.47As/In_0.52Al_0.48As quantum well, in which the expected beatings in the Shubinikov-de Haas oscillations of the longitudinal magnetoresistance R_xx were not observed. Zero-field spin splitting was extracted by measuring the weak anti-localization effect and the high field effective g-factor, g*, was extracted by fitting the tilt angle θ-dependent spacing of spin-splitted R_xx peaks. The Dingle plot is shown to be nonlinear, which can be attributed to the long-range scattering potential from the doping Be atoms near the substrate.