We discuss a new gravitational effect that the wave packet of a free-fall quantum particle undergoes a spin-dependent transverse shift in Earth’s gravitational field. This effect is similar to the geometric spin Hall effect(GSHE)(Aiello 2009 et al Phys. Rev. Lett. 103 100401), and can be called gravity-induced GSHE. This effect suggests that the free-fall wave packets of opposite spin-polarized quantum particles can be split in the direction perpendicular to spin and gravity.