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In this paper, we propose a new method to detect least significant bit (LSB) matching steganography which is based on neighbourhood node degree histogram characteristic function (NDHCF). First we calculate the center of mass (COM) of the NDHCF then embed another random secret message to compute the alteration rate of the NDHCF COM. We select NDHCF COM and the alteration rate as features and use support vector machines as a classifier. Experimental results demonstrate that the proposed method is efficient to detect the LSB matching stegonagraphy on compressed or uncompressed images and has superior results compared with other recently proposed algorithms.