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Lots of studies on synchronization focus on networks with static topologies, but ignore the synchronization in time-varying networks. We study the synchronization of the system in which agents carrying phase oscillators move in two-dimensional lattice with periodic boundary conditions and only interact with their neighbors. In particular, we assume that the direction of movement of an agent is positively correlated to the phase of the oscillator. By numerical simulations, we find cyclic oscillations in the phase transition to synchronization. Remarkably, the oscillators cluster spatially toward the oscillators with higher natural frequency to form groups. And the groups will collapse from the center, as coupling strength exceeds the critical value. In addition, we investigate the effect of moving speed on synchronization and find that the cyclic oscillation during synchronization will disappear with the increment of moving speed. • The direction of the moving Kuramoto oscillator was correlated with its phase. • The cyclic oscillation of order parameter will emerge for a larger coupling strength. • The oscillators' frequency distribution will affect the formation of the final groups. • The cyclic oscillations will disappear as the speed of movement increases. [ABSTRACT FROM AUTHOR]