The purpose of this study is to understand the propulsion mechanism of a jellyfish during its swimming. We observed the motion of a jellyfish (Aurelia aurita) by a motion-capture camera, and measured the vector field of flow around a jellyfish by using a PIV (Particle Image Velocimetry) measurement. A jellyfish is considered to be principally propelled by a jet at the contracting phase of its motion. If that is true, it is interesting that a jellyfish never stops traveling even at the expanding phase. We found that a vortex ring with the opposite vorticity to shed vortex ring was inside a jellyfish body in the expanding phase. We discussed a cause of an increase in thrust force and keeping constant speed in the expanding phase.