The back-scattering from front edge diffraction contributes significantly to mono-static radar cross section under TE-polarization when the specular reflection of an object is eliminated by elaborate shaping. With the aim to suppress the back-scattering of thin metallic edge, we propose to achieve wideband radar cross section (RCS) reduction by integrating an absorbing structure (AS) in front of the edge. The unit cell of AS is composed of a longitudinal array of metallic strips with linearly decreasing lengths. Under TE-polarized illumination, spoof surface plasmon polariton (SSPP) can be excited with high efficiency. Due to the deep-subwavelength property of SSPP, electromagnetic waves are highly confined around the AS, leading to strong local field enhancement and hence to wideband absorption. In this way, back-scattering of the edge is suppressed and the mono-static RCS can be reduced significantly over wide band. To verify this method, we designed, fabricated and measured a prototype. The results of both simulation and measurement indicate that our proposal can significantly suppress edge scattering, whose RCS reduction more than 10 dB achieves at range of 8.8–17.8 GHz under TE polarization. This work provides a new alternative of suppressing edge diffraction and may find applications in electromagnetic compatibility, radar stealth, etc.