The trade-off between performance and stability in amorphous oxide semiconductor-based thin-film transistors (TFTs) has been a critical challenge, meaning that it is difficult to simultaneously achieve high mobility and stability under bias and light stresses. Here, an amorphous mixture of two indium-free BaSnO3 and ZnSnO3 compounds, a-(Zn,Ba)SnO3, is proposed as a feasible strategy to achieve high mobility and stability at the same time. The choice of BaSnO3 as a counterpart to ZnSnO3, a well-known In-free candidate in amorphous oxide semiconductors, is to improve structural order and oxygen stoichiometry due to the large heat of formation and to preserve electron mobility due to the same kind of octahedral Sn–O network. Our first-principles calculations indeed show that compared to pure a-ZnSnO3, BaSnO3 plays a crucial role in restoring structural order in both stoichiometric and O-deficient supercells without seriously damaging the conduction band minimum. The resulting features of a-(Zn,Ba)SnO3 reduce O-deficiency and the valence band tail states, which are known to be critically associated with instability. It is experimentally demonstrated that a-(Zn,Ba)SnO3-based TFTs simultaneously exhibit high mobility (>20 cm2 V–1 s–1) and remarkable stability against negative bias illumination stress (ΔVth: <0.9 V). Our results suggest that a-(Zn,Ba)SnO3 would be a strong In-free candidate for next-generation TFT display, replacing the conventional a-InGaZnO4.