We present a time-resolved tomographic reconstruction of the velocity field associated with pulsatile blood flow through a rotationally-symmetric stenotic vessel model. The in-vitro sample was imaged using propagation-based phase contrast with monochromated X-rays from a synchrotron undulator source, and a fast shutter-synchronized detector with high-resolution used to acquire frames of the resulting dynamic speckle pattern. Having used phase retrieval to decode the phase contrast from the speckle patterns, the resulting projected-density maps were analysed using the statistical correlation methods of particle image velocimetry (PIV). This yields the probability density functions of blood-cell displacement within the vessel. The axial velocity-field component of the rotationally-symmetric flow was reconstructed using an inverse-Abel transform. A modified inverse-Abel transform was used to reconstruct the radial component. This vector tomographic phase-retrieval velocimetry was performed over the full pumping cycle, to completely characterize the velocity field of the pulsatile blood flow in both space and time.