In this work, the directional excitation of acoustic graphene plasmons (AGPs) are numerically studied using finite element methods. In our proposed hybrid graphene-metal structure under oblique incidences, not only are AGPs excited efficiently, but also they are unidirectional propagating along a graphene monolayer. Although the symmetry AGPs dispersion relations are broken by oblique incidence, both left- and right-moved AGPs are excited simultaneously at a resonant wavelength due to almost equaled wavenumbers of directional propagated AGPs. Based on the fact that great AGPs excitation efficiency can’t guarantee high EM energy propagating in one direction, we will focus on how the directional propagating net energy are affected by geometrical parameters. Due to the tunable graphene conductivity, AGPs propagation with great unidirectional net energy can be dynamically controlled by a relatively low externally applied bias voltage (electrostatic gating). The prototype structure may find applications in ultra-confined plasmon launchers and switchers in integrated optics.