Incoherent digital holography (IDH) with a sequential phase-shifting method enables high-definition 3D imaging under incoherent lights. However, sequential recording of multiple holograms renders IDH impractical for 3D videography. In this study, we propose grating-based in-line geometric-phase-shifting IDH. Our method divides orthogonal circularly polarized lights into four copies with a fabricated phase grating and subsequently creates self-interference holograms with geometric phases introduced by a segmented linear polarizer. This enables single-shot recording of holograms without the need for a specially designed image sensor, such as a polarization-sensitive sensor. Moreover, the achievable spatial resolution is higher than that of off-axis methods. As a proof-of-principle experiment, we demonstrated snapshot and video recording of 3D reflective objects using our IDH method. The results confirmed the feasibility of the proposed method.