In recent years, compression steganography technology has attracted the attention of many scholars. Among all image compression method, absolute moment block truncation coding (AMBTC) is a simple and effective compression method. Most AMBTC-based reversible data hiding (RDH) schemes do not guarantee that the stego AMBTC compression codes can be translated by the conventional AMBTC decoder. In other words, they do not belong to Type I AMBTC-based RDH scheme and easily attract malicious users’ attention. To solve this problem and enhance the hiding capacity, we used (7,4) hamming code to design a Type I AMBTC-based RDH scheme in this paper. To provide the reversibility feature, we designed a prediction method and judgement mechanism to successfully select the embeddable blocks during the data embedding phase and data extraction and recovery phase. In comparing our approach with other BTC-based schemes, it is confirmed that our hiding capacity is increased while maintaining the limited size of the compression codes and acceptable image quality of the stego AMBTC-compressed images.