Terahertz wave is defined as the far-infrared electromagnetic (EM) radiation between 0.1 and 10 THz. It has attracted increasing attention in both fundamental research and technological applications for its unique characteristics. In terahertz telecommunication, radar and imaging systems, terahertz antenna is key for the performance. To date, reported terahertz antennas suffer from limited phase modulation, relatively low efficiency and small beaming angle. Here we address these challenges by first designing three types of terahertz graphene antennas with the smallest size of 5 μm. We then propose a novel type of antenna with dual resonances, and achieve dynamic phase modulation within the full 2π range and meanwhile high efficiency above 20%. This performance surpasses antennas with single resonance since dual resonances alleviate the contradiction between large phase modulation range and high efficiency. We prepared terahertz graphene antennas with standard micro-fabrication processes, and experimentally obtained terahertz dynamic phase modulation of 1.03 THz with reflection efficiency above 23%, which agree with the simulation results. Making use of the phase modulation metasurfaces tuned according to continuous phase coding, we numerically realized terahertz beam steering with dynamic range of -25°~25°. We expect this work will provide a strategy for achieving large-range phase modulation and beam steering beyond the terahertz regime.