Hyperspectral imagery target detection has an important theoretical research value and application prospect, and it is a hot topic in the field of the remote sensing information processing. At present, most detection algorithms need to set an appropriate decision threshold, which is set by hand or computed by using the objects and background information. In practice, the little prior knowledge of the background often limits the application of many algorithms. To solve this problem, a new pure-pixel target detection algorithm for hyperspectral image is presented, which is based on the support vector data description (SVDD). Then the target detection problem is transformed to one-class classification problem. Firstly, SVDD classifier is trained by selected samples, and then the data are classified into inner-class (the target) and outer-class (the background). Next, the spatial characteristics of the target are used to reduce false alarm rate of the classified image. Finally, the ultimate detection results can be obtained. Experimental results of the hyperspectral data show that compared with the two classical spectral angle mapping and constrained energy minimization methods, the proposed method, which only requires a small number of target training samples, can reach the close results as the two algorithms when the optimal threshold values are selected. When the background samples increase, the method is superior to the mentioned two algorithms.