Embedding secret information into quantum carrier image for covert communication is one of significant research fields of quantum secure communication. Using good imperceptibility and high embedding efficiency of matrix coding, this paper proposes a novel matrix coding-based quantum steganography algorithm for quantum color images. In order to better apply matrix coding in actual demand, two different embedding methods are proposed. One embedding method is single pixel-embedded (1, 3, 2) coding, called SPE (1, 3, 2) coding for short. This method embeds two qubits of secret information into three least significant qubits (LSQbs) of a single pixel of quantum carrier image, and at most only one LSQb would be changed. The other embedding method is the multiple pixels-embedded (1, 3, 2) coding, called MPsE (1, 3, 2) coding, in which three LSQbs of multiple carrier pixels are utilized to embed two secret qubits. On account of experimental simulation obtained in the MATLAB environment, it shows that the new algorithm has good performance in the imperceptibility, the security, the embedding efficiency, and the embedding capacity. INDEX TERMS Quantum image steganography, matrix coding, quantum color images, imperceptibility, embedding efficiency.