Plasmonic structures that support the spoof surface plasmon polariton (SSPP) mode can be tailored to achieve strong absorption of electromagnetic (EM) waves. In particular, the profile of an absorbing plasmonic structure (APS) plays an important role in realizing its wideband absorption performance. In this paper, we propose a method of optimizing the longitudinal profile of APS based on Genetic Algorithm (GA), with the aim of obtaining high-efficiency wideband absorption of EM waves. The APS unit cell is composed of a longitudinal array of metallic strips, the length profile of which can be optimized to improve k-matching between free-space waves and SSPPs and meanwhile to customize absorption at each frequency within a wide band. Our investigation shows that non-linear variation of the strip lengths will make better k-matching and wideband absorption. As an example, a wideband APS is demonstrated using this method. The simulated and measured results show that the absorbance is higher than 90% in 10–30 GHz, which convincingly verifies the effectiveness of this method. This method provides an efficient approach to the design of radar absorbing structures and can also be extended to optimized design of other metamaterials.