The mathematical model of the quantum reversible circuit is unitary matrix. Matrix can better reflect the quantum state evolution and the physical properties of quantum computation. Matrix transformation based algorithm for 4-qubit reversible logic circuit synthesis is proposed in this paper. The algorithm skillfully takes advantage of the matrix representation of quantum circuit and the circuit transformation rules of the adjacent matrix to construct 4-qubit circuit. Compared with the constructive algorithm which is popular at present, the number of the gates in circuit constructed by our algorithm is less.