In this paper, we propose a graphene-covered subwavelength metallic grating where the Fermi level of graphene is sinusoidally modulated as a leaky-wave antenna at terahertz frequencies. This structure can convert spoof surface plasmon guided waves to free-space radiation due to the tunability of graphene. Analysis and design of the proposed leaky-wave antenna are discussed based on sinusoidally modulated surface impedance. The surface impedance is obtained by an analytical circuit model. The sinusoidal surface impedance is realized using modulation of the conductivity of graphene by applying a bias voltage. The proposed leaky-wave antenna is capable of electronic beam scanning with an almost constant gain and low sidelobe level by tuning the graphene Fermi level. In addition, a mode-converting section is proposed that drastically improves the return loss of the antenna.