Droplet behaviors on substrates with wettability controlled both in space and in time are numerically investigated by using the lattice Boltzmann method. Several typical droplet responses are found under different designs of substrate wettability control. Special attention is drawn to the conditions under which rapid transport of droplets can be achieved. It is found that on alternating non-wetting-wetting units with proper non-wetting confining stripes, this objective can be realized when the frequency of wettability switch approximately matches that of the droplet to move across one unit. The variation of the "optimal" frequency with the size of the confining stripe is sought within certain ranges. The various types of droplet movement are analyzed by looking at the three-phase lines on the substrate, as well as the droplet shapes under different conditions. The results may provide useful implications for droplet manipulation in microfluidic devices.