A line-imaging velocity interferometer has been implemented at the OMEGA laser facility of the Laboratory for Laser Energetics, University of Rochester. This instrument is the primary diagnostic for a variety of experiments involving laser-driven shock wave propagation, including high pressure equation of state experiments, materials characterization experiments, shock characterization for Rayleigh-Taylor experiments, and shock timing experiments for inertial confinement fusion research. Using a laser probe beam to illuminate a target the instrument measures shock breakout times and Doppler shifts in the reflected light. Velocities of interfaces, free surfaces and of shock fronts traveling through transparent media can be measured for velocities ranging from 0.1 to greater than 50 km/s with accuracies ∼ 1% over most of this range. Quantitative measurements of the optical reflectance of ionizing shock fronts can also be obtained simultaneous with the velocity measurements.