In order to overcome the deficiency of transistors or electronic switches in terahertz band, graphene is used in a terahertz reconfigurable antenna. Based on the model of graphene surface conductivity, the relationships of its surface conductivity to frequency, chemical potential and temperature, and the relationship between surface impedance and chemical potential are analyzed. Analysis of these relathionships proves the advantages of utilizing graphene in reconfigurable antennas. A graphene-based antenna with reconfigurable radiation pattern via applying external biased voltage is designed. The structure consists of a metal dipole (active element) and two metal with graphene dipoles as a reflector and a director. By altering chemical potential (external biased voltage), the states of graphene impedance configured in passive elements are adjusted and their current distribution is changed, which converts the passive ones between a reflector and a director. At last, through simulation and optimization of HFSS, the antenna realizes radiation with directions of 0°，±32°，±37°，±40°, operation frequency in (1.07±0.06) THz, relative impedance bandwidth over 7.84% and the maximum radiation efficiency of 89.96%. The maximum radiation gain has reached up to 8.312 dB at these seven radiation directions. This design has advantages as small size, light weight, simple and stable control, and offers a certain application value to beam-reconfigurable antenna in terahertz.