New asymmetric quantum generalized Reed-Solomon (RS) codes with parameters [[N = mn, K = m(2k — n + c), d z ≥ d/d x ≥ [d — c)]] q , where q is a prime power, l c+1, c ≥ 1, m ≥ 1 are integers, are constructed in this paper. These new codes can be utilized in quantum channels having great asymmetry.