A frequency-reconfigurable graphene patch antenna working in the terahertz band is designed on a polyimide substrate. The resonance frequency points of this antenna can be tuned dynamically by the bias electrical field rather than any electronic switch, meanwhile its radiation performance is kept. The main characteristics of graphene are studied, the input impedance of the graphene patch antenna is calculated based on the equivalent circuit model, and the reason of frequency-tuning is explained theoretically. The designed graphene antenna achieves five resonance frequency points in the terahertz band, which covers the frequency bands ranging from 678.25 GHz to 721.75 GHz. The radiation gain peak can reach 6.92 dB, and the radiation efficiency can reach 86.48%.