For some operator A ∈ B(H), positive integers m and k, an operator T ∈ B(H) is called k-quasi-(A, m)-symmetric if T * k (m j=0 (−1) j (m j)T * m−j AT j)T k = 0, which is a generalization of the m-symmetric operator. In this paper, some basic structural properties of k-quasi-(A, m)-symmetric operators are established with the help of operator matrix representation. We also show that if T and Q are commuting operators, T is k-quasi-(A, m)-symmetric and Q is n-nilpotent, then T + Q is (k + n − 1)-quasi-(A, m + 2n − 2)-symmetric. In addition, we obtain that every power of k-quasi-(A, m)-symmetric is also k-quasi-(A, m)-symmetric. Finally, some spectral properties of k-quasi-(A, m)-symmetric are investigated.