Particle motion in viscous fluids is a common and fascinating phenomenon. The hydrodynamics of a trapped finite-size particle recirculating along a stable orbit within a microvortex is still puzzling. Herein we report experimental observations of the orbiting motion of a finite-size particle in a vortex confined in a microcavity. The orbiting particle keeps crossing the streamlines with acute changes in velocity along the orbit, which can be divided into three stages: acceleration, swerving, and following. By examining the relationship between particle orbit and vortex streamlines, we uncover a particle slingshot effect and slip motion. Particle motion and vortex structure in three dimensions are also studied, revealing many new fascinating particle motion phenomena. The results provide new insights into the physics of particle motion in vortices.