This paper mainly investigates some properties of Cheng projection, which was proposed recently by Prof. Cheng to reduce the dimension of vector. As a linear transformation from the original vector space to the target vector space, the matrix representation of Cheng projection is given. Then, the structure matrix of Cheng projection, called the Cheng projection matrix, is obtained. Algebraic properties of Cheng projection are derived via its projection matrix. Furthermore, the product and norm of Cheng projection matrices are concerned.