In this paper, we propose a method for separating known targets of interests from the background in hyperspectral imagery. More precisely, we regard the given hyperspectral image (HSI) as being made up of the sum of low-rank background HSI and a sparse target HSI that contains the known targets based on a pre-learned target dictionary specified by the user. Based on the proposed method, two strategies are outlined and evaluated independently to realize the target detection on both synthetic and real experiments.