With the rapid development of smartphones, cloud storage, and wireless communications, protecting the security of compressed images through data transmission on the Internet has become a critical contemporary issue. A series of data hiding methods for AMBTC compressed images has been proposed to solve this problem. However, most of these methods either change the file size of the final compressed code or exchange the order of two quantization values in some blocks. To reverse this situation, this paper proposes a data hiding method for strict AMBTC format images using a hybrid strategy: replacement, matrix encoding, and symmetric quantization value embedding for three block types i.e., smooth blocks, less complex blocks and highly complex blocks. According to the hybrid strategy, an efficient data hiding order is designed to achieve higher-fidelity. Experimental results show that our proposed method provides an excellent balance between image quality and hiding capacity and has no error blocks in the final stego-compressed code.