To obtain 3D MR angiography having high contrast between vessel and stationary background tissue, a novel technique called sliding time of flight (TOF) is proposed. The proposed method relies on the property that flow-related enhancement (FRE) is maximized at the blood-entering slice in an imaging slab. For the proposed sliding TOF, a sliding stack-of-stars sampling and a dynamic MR image reconstruction algorithm were developed. To verify the performance of the proposed method, in-vivo study was performed and the results were compared with multiple overlapping thin 3D slab acquisition (MOTSA) and sliding interleaved ky (SLINKY). In MOTSA and SLINKY, the variation of FRE resulted in severe venetian blind (MOTSA) or ghost (SLINKY) artifacts, while the vessel-contrast increased as the flip angle of RF pulses increased. On the other hand, the proposed method could provide high-contrast angiograms with reduced FRE-related artifacts. The sliding TOF can provide 3D angiography without image artifacts even if high flip angle RF pulses with thick slab excitation are used. Although remains of subsampling artifacts can be present in the reconstructed images, they can be reduced by MIP operation and resolved further by regularization techniques.