A novel dual-beam terahertz (THz) leaky-wave antenna (LWA) based on triple-periodically (TP) modulated spoof surface plasmon (SSP) waveguide is proposed. It is shown that SSP can be effectively excited and propagated along the surface of parallel corrugated metallic strips. Through proper design, the n=?1 and n=?2 Floquet modes are brought into the leakage radiation region simultaneously. Consequently, the forward and backward propagating waves corresponding to the two modes respectively generate two radiation beams in the far-field region. The proposed antenna is capable of steering the forward beam within a range of 34° and the backward beam within a range of 48° when frequency is swept between 0.23 THz and 0.29 THz. A simulated peak gain of 11.4 dBi and gain variation of 2.87 dBi are achieved within the band. The proposed LWA can be applied in THz wireless communication and radar systems.