The high degree of freedom in leg systems enables quadruped robots to provide superior mobility and gait robustness. Therefore, quadruped robots are regarded as a new means of transportation over rough terrain. One of the most promising applications of quadruped robots may be precise surveillance in military and disaster environments. For this purpose, the vibration of the robot body, which is unavoidable due to the repeated ground contact, should be suppressed. This paper proposes a vibration suppression control algorithm for the head suspension system of a quadruped robot. Using inertial measurement units (IMUs), the vertical velocity of the end point of the head suspension system is estimated with high reliability. The head suspension system is controlled to regulate the absolute vertical velocity of the end point of the head suspension system, i.e., a camera. The proposed absolute velocity estimation method is verified using an external camera and encoder. Finally, the vibration suppression control algorithm is verified with a quadruped robot called the Cheetaroid-I Carrier.