Topological insulator (TI) is a peculiar phase of matter exhibiting excellent quantum transport properties with potential applications in lower-power-consuming electronic devices. Searching for inversion-asymmetric quantum spin Hall (QSH) insulators persists as an effect for realizing new topological phenomena. Using first-principles density functional theory calculations, we investigate the geometry, dynamic stability, and electronic structures of monolayer β-BiSb. We find that it presents QSH state under biaxial tensile strain of 14%. The nontrivial topological situation in the strained system is confirmed by the identified band inversion, Z₂ topological invariant (Z₂ = 1), and an explicit presence of the topological edge states. Owning to the asymmetric structure, remarkable Rashba spin splitting is produced in both the valence and conduction bands of the strained system. These results provide an intriguing platform for applications of monolayer β-BiSb in future alternative quantum Hall spintronic devices.