The theory of linear suboptimal output feedback control with a frequency-shaped cost functional is applied to the vibration control of a vehicle model subjected to the input of the roughness of road surface. The feedback control gain is obtained with respect to a quadratic cost functional whose weighting matrices are functions of frequency. In the control using a frequency-shaped cost functional, the vibration frequency components can be reduced over specific bands of frequencies. Janeway and ISO human response curves with respect to acceleration are used to examine the vibration characteristics of a controlled vehicle model. The theory of the suboptimal control problem subjected to control structure constraints is applied to the synthesis of the output feedback control system. The theoretical and simulated results of the suboptimal output feedback control with a frequency-shaped cost functional are compared with those of the optimal control without a frequency-shaped cost functional and with state estimation using a Kalman filter.