A novel model using the transfer matrix method for multibody system (TMMMS) is put forward to describe the dynamic characteristics of a cantilever beam that has a concentrated mass at its tip under axial excitations. The theoretical analysis and numerical results demonstrate that this model has some advantages, such as for a small matrix and a higher computational speed. Based on this model a control system, which is composed of a LQG controller, a piezoelectric actuator, and a sensor for the cantilever beam is proposed, theoretically analyzed, and experimentally verified. The experimental results show that the proposed controller with the piezoelectric actuator can effectively reduce the vibration of the cantilever beam with an eccentric tip mass. The piezoelectric sensor can measure vibration responses with high-accuracy. Therefore, this new model gives a broad range of possibilities for model-based controller design and implementation.