This paper is concerned with vibration control for elevating motions of a truck crane by using multi-body dynamics (MBD) theory. The MBD theory represents behavior of machinery by differential algebraic equations (DAEs). The variable constrained control (VCC) has been applied to the MBD systems. When the positioning and swing control of a suspended load are simultaneously performed by only elevating motion of the crane boom, the crane is regarded as an under-actuated system. VCC and PD control which has variable gains adjusted by neural network (NN) are combined to accomplish the both objects. Validity of the novel combined procedure of VCC and PD with variable gains is verified by numerical calculations. The proposed controller is definitely applied to an experimental crane model.