Measurement of blood flow by cine phase-contrast MRI is a valuable technique in the study of arterial disease but is time consuming, especially for multi-slice (4D) studies. Compressed sensing is a modern signal processing technique that exploits sparse signal representations to enable sampling at lower than the conventional Nyquist rate. It is emerging as a powerful technique for the acceleration of MRI acquisition. In this study we evaluated the accuracy of phase-contrast carotid blood flow measurement in healthy volunteers using threefold undersampling of kt-space and compressed sensing reconstruction. Sixteen healthy volunteers were scanned at 1.5T with a retrospectively gated 2D cine phase-contrast sequence. Both fully sampled and three-fold accelerated scans were carried out to measure blood flow velocities in the common carotid arteries. The accelerated scans used a k-t variable density randomised sampling scheme and standard compressed sensing reconstruction. Flow rates were determined by integration of velocities within the manually segmented arteries. Undersampled measurements were compared with fully sampled results. Bland-Altman analysis found that peak velocities and flow rates determined from the compressed sensing scans were underestimated by 5% compared with fully sampled scanning. The corresponding figure for time-averaged flow was 3%. These acceptably small errors with a threefold reduction in scan time will facilitate future extension to 4D flow studies in clinical research and practice.