This paper shows a design method of a nonlinear controller for linear systems. In order to design a nonlinear controller, we use a nonlinear weight and consider the H_∞ control problem. It is shown that, under some constraints on the nonlinear weight, a nonlinear controller can be obtained by solving the Algebraic Riccati Inequality. And some of admissible nonlinear weights are shown. The obtained nonlinear controller is a low (high) gain controller at around the origin, and becomes a high (low) gain controller at far from the origin.