This paper proposes an innovative and novel steganography method for an AMBTC compressed image by combining a turtle-shell reference matrix and (7, 4) Hamming code, called hybrid strategy and block feature-based data hiding method (HBF-DH). Firstly, the proposed method compresses an original image by an AMBTC compression technique, and then applies a user predefined threshold pair to classify all compressed blocks into three categories: a smooth block, less complex block, and high complex block. Next, the smooth and less complex blocks are smoothed out with the aim of vacating more space for data hiding. The embedding process is divided into two phases. In the first phase, each quantization level pair of the AMBTC compression codes is used to embed an 8-ary secret digit by using a restrictive turtle-shell reference matrix. The second phase embeds binary secret data into a bitmap according to block characteristics. For smooth blocks, the bitmap is directly replaced as binary secret data by using bit replacement. For a less complex block, the binary secret data is concealed into a bitmap by using our proposed (7, 4) Hamming code based data hiding strategy, which increases the data hiding capacity without significant impact on image quality. The experimental results and analyses prove that the proposed HBF-DH method is superior to other existing AMBTC based data hiding methods in terms of data hiding ability with satisfactory image visual quality.INDEX TERMS Steganography, AMBTC, (7, 4) hamming code, turtle-shell reference matrix, high payload, block features.