Existing sparsity-based hyperspectral image (HSI) target detection methods have two key problems. 1) The background dictionary is locally constructed by the pixels between the inner and outer windows, surrounding and enclosing the central test pixel. The dual-window strategy is intricate and might result in impure background dictionary deteriorating the detection performance. 2) For an unbalanced binary classification problem, the target dictionary atoms are generally inadequate compared with the background dictionary, which might yield unstable performance. For the issues, this article proposes a novel structurally incoherent background and target dictionaries (SIBTD) learning model for HSI target detection. Specifically, with the concept that the observed HSI data is composed of low-rank background, sparsely distributed targets, and dense Gaussian noise, the background and target dictionaries can be jointly derived from the observed HSI data. Additionally, the introduction of structural incoherence can enhances the discrimination between the target and background dictionaries. Thus, the developed model can not only lead to a pure and unified background dictionary but also augment the target dictionary for improved detection performance. Besides, an efficient optimization algorithm is devised to solve SIBTD model, and the performance of SIBTD is verified on three benchmark HSI datasets in comparison with several state-of-the-art detectors.