The grid-interconnected microgrid can be able to operate with and without the utility microgrid to supply electricity. when the microgrid operates in grid-connected mode, the frequency of the microgrid synchronizes with the system frequency. In this case, the frequency of the microgrid has small variation which is able to change the output of distributed generation with a droop controller. Thus, the small variation of frequency can make the distributed generation generate unnecessary electricity consistently. In this paper, we propose a frequency droop control with a dead band so as to prevent the distributed generations from generating unnecessary output while in grid-interconnected mode. In addition, a distributed generation can have a restoration control to restore the frequency changed by a droop control as a rated frequency. Also, we state the problem of restoration control with a dead band, and propose its solution when the microgrid operates in stand alone mode. We simulate the proposed droop control using PSCAD/EMTDC to verify the validity of the control.