In this paper, we consider the Neumann problem of a class of mixed complex Hessian equations σ k (∂∂u) = k−1 l=0 α l (x)σ l (∂∂u) with α l positive and 2 ≤ k ≤ n, and establish the global C 1 estimates and reduce the global second derivative estimate to the estimate of double normal second derivatives on the boundary. In particular, we can prove the global C 2 estimates and the existence theorems when k = n.Mathematical Subject Classification (2010): Primary 35J60, Secondary 35B45.