With the use of large eddy simulation (LES), the initial structure and mixing characteristics of both the subsonic and supersonic circular jets are studied, respectively. The stretched-vortex model combined with the high-order hybrid scheme is employed to solve the LES equations. The typical structures of the initial jet at different conditions have been presented and discussed. The formation and evolution process of the vortex ring has been displayed in detail, and the unique characteristics of a compressible vortex ring generated by the unsteady jet have been identified. Furthermore, the engulfment and mixture of ambient gas with the jet gases have been discussed, the different mixing processes of both subsonic and supersonic jets, especially the shock wave effect in a supersonic jet on mixing process, have been illustrated.