The eigenvalues of a normal matrix are not sensitive to its elements perturbation. Based on the fact, the pole normal assignment problem for linear control systems is discussed. The aim is to find a state feedback control law. When the closed-loop system has desired poles and the closed-loop system matrix is a normal matrix, the robustness of the control system is enhanced. For linear constant systems, a necessary and sufficient condition is given to normal assignment of the desired poles. When the condition holds, a unified expression of the state feedback control laws is showed. An example is given for illustration of the proposed algorithm.