The plasmonic waveguide made of uniform corrugated metallic strip can support and guide spoof surface plasmon polaritons (SSPPs) with high confinements. Here, we propose periodically-modulated plasmonic waveguide composed of non-uniform corrugated metallic strip to convert SSPPs to radiating waves, in which the main beam of radiations can steer continuously as the frequency changes. To increase the radiation efficiency of the periodically-modulated plasmonic waveguide at the broadside, an asymmetrical plasmonic waveguide is further presented to reduce the reflections and realize continuous leaky-wave scanning. Both numerical simulations and experimental results show that the radiation efficiency can be improved greatly and the main beam of leaky-wave radiations can steer from the backward quadrant to the forward quadrant, passing through the broadside direction, which generally is difficult to be realized by the common leaky-wave antennas.