AbstractWe show that quantum spin Hall (QSH) effect does not occur in a square lattice model due to cancellation of the intrinsic spin-orbit coupling coming from different hopping paths. However, we show that QSH effect can be induced by the presence of staggered magnetic fluxes alternating directions square by square. When the resulting Peierls phase takes a special value "Equation missing", the system has a composite symmetry ΘΡ−"Equation missing" with Θ the time-reversal operator and Ρ−"Equation missing" transforming the Peierls phase from γ to γ − "Equation missing", which protects the gapless edge states. Once the phase deviates from "Equation missing", the edge states open a gap, as the composite symmetry is broken. We further investigate the effect of a Zeeman field on the QSH state, and find that the edge states remain gapless for "Equation missing". This indicates that the QSH effect is immune to the magnetic perturbation.