We consider the problem of synchronizing a general complex network by means of the on-off coupling strategy; in this case, the on-off time scale is varied from a very small to a very large value. In particular, we find that when the time scale is comparable to that of node dynamics, synchronization can also be achieved and greatly optimized for the upper bound of the stability region which nearly disappears, and the synchronization speed is accelerated a lot, independent of network topologies. Our study indicates that the time scale for network variation is of crucial importance for network dynamics and synchronization under the comparable time scale which is much more advantageous over other time scales. Both analysis and experiments confirm the conclusions.