For some difficult sample sets with different distribution properties, fast decision algorithms of support vector data description(SVDD) may obtain low classification accuracy. Therefore, a fast decision algorithm of SVDD based on the hyper-ellipse classification boundary is proposed, which can reduce the testing complexity from $O(n)$ to O(2) (n is the support vector number). The disadvantages of current decision methods are presented, and then the method of constructing the hyper-ellipse classification boundary is proposed. Experimental results on multi-datasets show that the proposed method can largely improve the classification accuracy and the applicability of existing fast decision algorithms.