We report on the first experiments on saturable absorption in graphene at microwave frequency band. Almost independent of the incident frequency, microwave absorbance of graphene always decreases with increasing the power and reaches at a constant level for power larger than 80 µW, evidencing the microwave saturable absorption property of graphene. Optical saturable absorption of the same graphene sample was also experimentally confirmed by an open-aperture Z-scan technique by one laser at telecommunication band and another pico-second laser at 1053 nm, respectively. Herein, we are able to conclude that graphene is indeed a broadband saturable absorber that can operate at both microwave and optical band.