In order to solve the problem of the complex form and complicated calculation of the design matrix for high-dimensional mixture experiments, the definition of the permutation matrix is proposed by using high-order mixture lattice points as the support set. Firstly, the method to construct the design matrix from the permutation matrix is discussed, and the representation of the information matrix and the correlation matrix are derived. Then, the properties of the determinant, trace, and eigenvalue of the permutation matrix are studied. Finally, the effectiveness of the permutation matrix for the analysis of mixture design is verified, and the necessity and feasibility of using the permutation matrix to construct a high-order lattice point set and an optimal design are further analyzed.