Based on the mechanism of the Surface Plasmon Amplification by Stimulated Emission of Radiation (SPASER), an off-centre gold shell nanoantenna consisted of the silica-gold-silica three-layer core-shell was proposed and its multi-wavelength light scattering characteristics were numerically analyzed by using the Finite Element Method (FEM). For the SPASER-based nanoantenna, the results show that, the scattering wavelength number increases with the increasing of the silica core eccentricity and the scattering light intensity is greatly enhanced. When the eccentricity of silica core is 9 nm, the proposed nanoantenna has four intensity resonance peaks which are located at 615 nm, 656 nm, 724 nm and 847 nm respectively, and the corresponded scattering intensities are much higher than that of the non-SPASER one, about 104 times. Moreover, the scattering wavelengths of the proposed nanoantenna can be easily adjusted by changing the polarization angle of the incident light. The SPASER-based nanoantenna would be useful to design the multi-wavelength laser devices in nanoscale.