The behaviors of a neutrally buoyant ellipsoidal particle in vortical flow confined by a microcavity are numerically studied using the Lattice-Boltzmann method. For specific initial position, an isolated ellipsoid may develop a stable limit cycle orbit inside microcavity due to the interaction between particle and the carrier flow. It is observed that ellipsoidal particles of different shapes exhibit two different stable rotational modes depending on the initial orientation and lateral position. A prolate spheroid tends to enter a tumbling mode whereas an oblate spheroid is apt to achieve a rolling mode. The evolution of rotational velocities along the stable orbit is also analyzed for particles of different shapes.