A wideband and wide-angle beam-scanning antenna with low sidelobe levels (SLL) fed by spoof surface plasmon polaritons (SSPP) is designed. The SSPP feeding lines are adopted to excite the oval radiating patch array in the fast wave zone, whereas its low loss transmission in the slow wave zone is used to excite the spoof plasmonic antipodal Vivaldi antenna (AVA), realizing the beam scanning angle of 180° within 4~12 GHz (a relative bandwidth of 100%). And by arranging the oval radiating patches in a tapered way, the SLL during leaky-wave radiation is effectively reduced. The simulation results show that the SLL of the designed full-angle beam-scanning antenna is below -10 dB within the 4~12 GHz frequency band. Such antenna has considerable potential in application under condition of radar detection and target tracking.