In this paper, a tunable cantilever plate structure is presented, in which a box is attached to each corner of its free sides and a ball is placed in each box. Change of the balls position makes natural frequency of the structure variable, which expands working bandwidth of the structure to accommodate the complex ambient vibration. The modal analysis of the tunable cantilever plate is carried out by the finite element software-ABAQUS. Changing the balls position, it is found that there are maximum and minimum values in the natural frequency of the self-tuning structure, which forms a resonance bandwidth. Moreover, there are multiple position combinations of two balls at the same natural frequency in the range of resonance band. The paper studies the influence of mass and geometrical dimensions of boxes and balls on the natural frequency and bandwidth. While ensuring strength and stiffness of the structure, optimal material and size parameters are selected to improve the resonant bandwidth. This provides a theoretical basis for applying the tunable structure to piezoelectric energy harvester.