This paper considers reduced-order controllers for a class of mixed H 2 /H∞ control problem. There is a new controller degree bound for the H ∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows the following important result: If the mixed H 2 /H∞ problem is solvable, then there must exist reduced-order controllers with orders less than that of generalized plant. Moreover, we can also give new feasible LMI-based design methods for constructing the reduced-order controller because of the constructive proof, which only involve algorithms and convex optimizatin of LMI. The result developed in this paper are valid both for the continous- and discrete-time mixed H 2 /H∞ control problems. This paper suggests reduced-order controllers for a class of mixed H 2 / H∞ control problem. There is a new controller degree bound for the H ∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows the following important result: If the mixed H2 / H∞ problem is solvable, then there must exist reduced-order controllers with orders less than that of generalized plant. , we can also give new feasible LMI-based design methods for constructing the reduced-order controller because of the constructive proof, which only involve algorithms and convex optimizatin of LMI. The result developed in this paper are valid both for the continous- and discrete -time mixed H 2 / H∞ control problems.