The traditional random vibration test with frequency domain method aims to generate a stationary and Gaussian vibration environment. But the practical vibration environments are always superGaussian, especially the wind load of transmission towerline system, which can cause different damages to the structures compared with Gaussian excitations. Thus, it is significant to study the superGaussian test method. The research of characteristics of superGaussian linear system response is the key to superGaussian environment vibration test, and is the basis of PSD and kurtosis repetition. The response of the linear system excited by superGaussian signals is studied, the formulas of response kurtosis are derived in both time and frequency domain. The concrete expression of the single degree of freedom linear system response kurtosis is displayed. This formula indicates that the superGaussian characteristics of the linear system response is related to excitation’s superGaussian characteristics and system damping ratio, and the conclusion is verified by simulations. Phase selection method and traditional PSD decomposition method are used to generate superGaussian driving signal according to reference power spectrum density and kurtosis. Finally, a SISO cantilever beam control experiment results indicate that the error between output response spectrum and reference spectrum based on the proposed control algorithm meets the requirement ± 3dB in engineering, and the kurtosis meets the reference requirement.