An efficient data hiding method with modulo-2 operation and Hamming code (3, 2) based on absolute moment block truncation coding (AMBTC) is proposed. In order to obtain good data hiding performance, different textures are assigned to different embedding strategies. The AMBTC compressed codes are divided into smooth and complex blocks according to texture. In the smooth block, the secret data and the four most significant bits plane of the two quantization levels are calculated using modulo-2 operation to replace the bitmap in order to improve the security of data transmission. Moreover, Hamming code (3, 2) is used to embed the two additional secret bits in the three significant bits planes of the two quantization levels. In the complex block, one secret bit is embedded by swapping the order of two quantization levels and flipping the bitmap. Experimental results show that the proposed method achieves higher capacity than the existing data hiding methods and maintains good visual quality.