We design a four-reflector offset antenna satisfying the cross-polarization elimination condition and the broadband characteristics condition which consists of one primary horn, three subreflectors and one main reflector. The cross-polarization elimination condition for the four-reflector offset antennas is expressed by the equations of hyperbolas with the coordinate axes of the reciprocal of equivalent focal lengths. The configurations of the reflector system are derived simply from the graphical representation because four-reflector offset antennas satisfying these relationships exist on the hyperbolas with the coordinate axes of the reciprocal of equivalent focal lengths. Furthermore, we clarified that the derived condition for having planar phase front applying the broadband characteristics condition is independent of frequency. An actual design example for the four-reflector offset antennas satisfying the cross-polarization elimination condition and the condition for having planar phase front, both of which are independent of frequency is shown. The design method using the graphical representation is simpler than that of the tri-reflector offset antennas.