Airborne hyperspectral data have both high spectral and spatial resolutions. Although the finer spatial resolution allows more abundant spatial characteristics to be exhibited, the spectral variability problem remains. However, few of the current spatial-spectral target detection methods can fully exploit the spatial information while solving the spectral variability problem. In this paper, a sparse spatial-spectral conditional random field (CRF) target detection framework for airborne hyperspectral data, namely S3CRF, is proposed to address these problems, in which the unary and pairwise potential functions are designed accordingly. To model the spatial information in a larger neighborhood while solving the spectral variability problem, an object-oriented strategy is introduced to modify the residual map obtained by sparse representation. For the pairwise potential function, the adaptive local eight-neighborhood structure is constructed considering the neighboring spatial correlations. Furthermore, global spatial-contextual information is captured through the inference of S3CRF. Finally, the a posteriori probability of each pixel belonging to the target is utilized for the target detection. The experiments undertaken in this study confirmed that the proposed method can effectively suppress the background while achieving a competitive quantitative and qualitative target detection performance.