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This paper presents a new design approach of a gain-scheduling controller using only frequency responses of the plant without any transfer functions or state space representations of the plant. In this paper, the robust performance condition is approximated by convex constraints with respect to the controller parameters on the Nyquist diagram, and controller parameters that satisfy convex constraints are derived by solving convex optimization problem. A gain-scheduling controller is linearly parameterized with respect to a controller parameter vector defined as an affine function of the scheduling parameter. Moreover, the proposed method can reduce conservativeness by design of the optimal nominal model from the obtained frequency responses at the prespecified frequency points. The effectiveness of the proposed method is confirmed through the experiments.