We propose a beam reconfigurable micro-strip quasi-Yagi-Uda （QYU） antenna operating at terahertz （THz） frequencies. The antenna, on a metal-backed SiO₂ substrate, consists of a metallic micro-strip transmission line, a metallic reflector, a metallic half-round micro patch, and three groups of monolayer-graphene-patch directors. Because the conductivities of the graphene patches can be electrically tuned, the radiation direction of the QYU antenna can be dynamically controlled by adjusting the bias voltages applied to the graphene patches. The basic properties and the tunable behaviors of the antenna are systemically simulated and optimized. It has very fast modulation speed and very low return loss. In particular, the numerical results show that the main radiation lobe angle φ （azimuth angle） of the QYU antenna can be swept from 30° to 150° in θ=60° （zenith angle） plane with different configurations of bias voltages applied to the graphene-patch directors. The proposed antenna is very suitable for THz beam reconfigurable applications, such as phased array radar systems.