We present simulations of the vortex dynamics associated with the self-propelled motion of jellyfish. The geometry is obtained from image segmentation of video recordings from live jellyfish. The numerical simulations are performed using three-dimensional viscous, vortex particle methods with Brinkmann penalization to impose the kinematics of the jellyfish motion. We study two types of strokes recorded in the experiment. The first type (Stroke A) produces two vortex rings per stroke: one outside the bell during the power stroke and one inside the bell during the recovery stroke. The second stroke type (B) produces three vortex rings: one ring during the power stroke and two vortex rings during the recovery stroke. Stroke B is found to produce a faster motion than stroke A. The speed of the jellyfish scales with the square root of the Reynolds number.