An experimental setup and a simple reconstruction method are presented to measure velocity fields inside slightly tapering cylindrical liquid jets traveling through still air. Particle image velocimetry algorithms are used to calculate velocity fields from high speed images of jets of transparent liquid containing seed particles. An inner central plane is illuminated by a laser sheet pointed at the center of the jet and visualized through the jet by a high speed camera. Optical distortions produced by the shape of the jet and the difference between the refractive index of the fluid and the surrounding air are corrected by using a ray tracing method. The effect of the jet speed on the velocity fields is investigated at four jet speeds. The relaxation rate for the velocity profile downstream of the nozzle exit is reasonably consistent with theoretical expectations for the low Reynolds numbers and the fluid used, although the velocity profiles are considerably flatter than expected.