Surface plasmon polaritons (SPPs), the electromagnetic waves traveling along metal-dielectric or metal-air interface, which originate from the interactions between light and collective electron oscillations on metal surface, have received considerable attention for their promising applications in the future optical field, such as image, breaking diffraction limit, subwavelength-optics microscopy, lithography, etc. However, one of the fundamental issues in plasmonics is how to actively manipulate the propagation direction of SPPs. In this paper, we propose and numerically investigate a graphene-based unidirectional SPP coupler, which is composed of asymmetric plasmonic nanoantenna pairs with a graphene sheet separated by a SiO2 spacer from the gold substrate. The device geometry facilitates the simultaneous excitation of two localized surface plasmon resonances in the entire structure, and consequently, the asymmetric nanoantenna pairs can be considered as being composed of two oscillating magnetic dipoles or as two SPP sources. Because the resonance of the plasmonic antenna pairs depends on the bias voltage applied across graphene sheet and back-gated Au, the phase difference between radiated electromagnetic waves induced by the antenna can be tuned through varying the Fermi level of graphene. Here, approximately a n/2 phase difference between radiated electromagnetic (EM) waves can be acquired at EF 0.81 eV, which indicates that the radiated EM waves can interfere constructively along the direction of the x-axis while interfere destructively along the opposite direction. This directional propagation of EM wave leads to the unidirectional propagation of SPPs. Furthermore, electric field distribution of the cavity demonstrates that the tunability of plasmonic antenna is proportional to the electric field intensity in the vicinity of the graphene region. For our designed structure, the left cavity can provide a significantly larger tunable range than the right one. With this result, we can quantitatively analyze the tuning behavior of graphene-loaded plasmonic antenna based on equivalent circuit model, and draw the conclusions that the unidirectional SPP propagation effect originates from the interference mechanism. In addition, compared with the device reported previously, our proposed device possesses a huge extinction ratio (2600) and more broadband tunable wavelength range (6.3-7.5 m). In addition, it is possible to make up for the deficiencies of current nanofabrication technologies by utilizing its actively controlled capability. All the above results indicate that the proposed active device promises to realize a compactable, tunable, and broadband terahertz plasmonic light source. It will play an important role in future photonic integrations and optoelectronics.