To improve the security and reliability of Internet communications, a steganalysis algorithm for graphics interchange format (GIF) images is proposed in this paper. 36-dimensional statistical features of GIF image, which are sensitive to the color correlation between adjacent pixels and the breaking of image texture, are extracted based on differential zero coefficients (DZC) and index co-occurrence matrix (ICM). Support vector machine (SVM) technique takes the 36-dimensional statistical features to detect hidden message in GIF images effectively. Experimental results indicate that the proposed algorithm has better detection performance and higher time efficiency comparing with other similar steganalysis algorithms for typical steganographic algorithms including optimum parity assignment (OPA), sum of components (SoC), multibit assignment steganography (MBA) and steganographic tools which are popular in the Internet, such as EzStego, S-Tools4 and Gif-it-up. Furthermore, the proposed algorithm has the ability of universal steganalysis.