This paper proposes a single image-based face liveness detection method for discriminating 2-D paper masks from the live faces. Still images taken from live faces and 2-D paper masks were found to bear the differences in terms of shape and detailedness. In order to effectively employ such differences, we exploit frequency and texture information by using power spectrum and Local Binary Pattern (LBP), respectively. In the experiments, three liveness detectors utilizing the power spectrum, LBP, and fusion of the two were trained and tested with two databases which consist of images taken from live and four types of 2-D paper masks. One database was acquired from a web camera while the other was from the camera on the automated teller machine. Experimental results show that the proposed methods can efficiently classify 2-D paper masks and live faces.