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The propagation of a wave packet in a honeycomb photonic lattice has been studied using the time-dependent wave packet dynamics.It is found that the wave packet,superposed from the positive and negative energy modes at the vicinity of the two inequivalent Dirac points,can transform into a double-ring structure,which is caused by the interference between the two positive and negative energy modes around the Dirac points and is closely related to the Zitterbewegung (ZB).Also,a possible way to detect the ZB effect is proposed in the honeycomb photonic lattice.