The state of graphene loop applied in the slotted antenna radiator is converted from non-resonant to resonant to achieve the tunable band-notch characteristics in an ultra-wideband (UWB) antenna. In the non-resonant state, the graphene loop with value of chemical potential as 0 eV acts as a parasitic element and does not contribute to radiation. Increasing the chemical potential of graphene starts converting the state of graphene loop from non-resonant to resonant. The graphene surface starts confining the localized surface plasmons with the increment in chemical potential and hence the multiple higher order resonances are formed. The higher order resonance with the destructive effect provide the band-notch characteristic in UWB response. The variation in chemical potential can tune the created notched band over frequency. Also, conversion of state of graphene loop from non-resonant to resonant deteriorates the far-field radiation parameters and radiation efficiency of antenna drastically. A trade-off can be set to find the required value of gain and radiation efficiency and frequency of the created band notch. Moreover, another technique of utilizing the double graphene loops with less surface area has also been studied, which allows one to attain the higher radiation efficiency of antenna along with the band-notch characteristics.