Abstract: In this paper,we give the explicit expressions of level k(r₁ ,r₂ ,… ,r_k) circulant matrices of order n ₁n ₂…n _k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k(r₁ ,r₂ ,… ,r_k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.  摘要：In this paper,we give the explicit expressions of level k(r₁ ,r₂ ,… ,r_k) circulant matrices of order n ₁n ₂…n _k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k(r₁ ,r₂ ,… ,r_k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable. 

Key words:  level-k(r₁ ,r₂ ,…, r_k) circulant matrices；explicit expressions；eigenvalues；inverse  matrices