Absorption of electromagnetic waves in a medium is generally manipulated by controlling the frequency dispersion of constitutive parameters. However, it is still challenging to gain the desired constitutive parameters for customized absorption over a broad frequency range. Here, by virtue of spoof surface plasmonic polaritons (SPPs), we demonstrate capabilities of the spatial k-dispersion engineering for producing the customized broadband absorption. Incident waves can be efficiently converted to the spoof SPPs by plasmonic arrays, and their propagation and/or absorption can be controlled by engineering the spatial dispersion of k-vector. Based on this feature, we show how such concept is employed to achieve broadband as well as frequency-selective broadband absorptions as examples. It is expected that the proposed concept can be extended to other manipulations of propagating electromagnetic waves over a broad frequency range.