A robot crane truck is developed by the Bridge Inspection Robot Development Interface(BRIDI) for an automated and/or teleoperated bridge inspection. This crane truck looks similar to the conventional bucket crane, but is much smaller in size and light-weight. At the end of the telescoping boom which is 12m long, a robot platform is mounted which allows the operator to scan the bridge structure under the deck trough the camera. Boom vibration induced by wind and deck movement can cause serious problems in this scanning system. This paper presents a control system to mitigate such vibration of the robot boom. In the proposed control system, an actuator is installed at the end of the working boom. This control system is studied using a mathematical model analysis with LQ control algorithm and a scaled model test in the laboratory. The study indicates that the proposed system is efficient for the vibration control of the robot booms, thereby demonstrating its immediate applicability in the field.