A terahertz (THz) antenna with tunable filtering is designed and numerically studied. A slotted monopole radiator with defected ground structure is used for operating with wideband response with an impedance bandwidth in the range of 3.80-11.98 THz for S 11≤-10d B. A slot is engraved in the radiator for obtaining the filtering characteristics in the antenna response. By varying its chemical potential, the frequency band 5.05-6.69 THz with graphene material can provide the tunability in the frequency and bandwidth of the filtered band in the antenna response. Furthermore, the antenna can provide radiation efficiency of more than 90% and gain with a peak value of 6.6 dBi in the passband.