Internal cavitation flow was directly coupled to the corresponding jet in the volume-of-fluid large-eddy simulation (VOF-LES) to investigate the primary atomization process of the jet with cavitation. Numerical results showed that once cavitation clouds were ejected out of the nozzle, a portion of the cavitation cloud collapsed near the upper surface of the jet immediately. The collapse caused the top surface to be disordered with some liquid drops separating from the main jet, while the bottom surface remained stable for a long distance before being disturbed by the shedding cavitation cloud. Hence, the appearance of cavitation improved the primary atomization and led to an asymmetrical jet structure. To further study the asymmetrical atomization of the jet, the present research also performed spray simulations on the surface breakup of the major axis vertically oriented elliptical jets with different eccentricities. The atomization of the jet was evaluated by breakup rate (BR), a new parameter, which showed a declining trend with the increasing eccentricity. The contour spray angle also dropped gradually. Moreover, the horizontal contour spray angle of the elliptical jet was always higher than its vertical contour spray angle. The gap between the two contour angles increased gradually as the eccentricity increased. As a result, the atomization of the elliptical jet tended to be more asymmetrical.