A frequency-tuned dynamic vibration absorber by tuning stiffness to reduce vibration at some troubled resonance frequencies of a simply supported beam structure is designed in this paper. Both theoretical and simulation analysis of vibration absorption are conducted. On the basis of analyzing bending vibration of the simply supported beam structure, inherent characteristics and frequency response characteristics of the simply supported beam system before and after being fixed dynamic vibration absorber are obtained by using the energy method with Rayleigh-Ritz procedure of flexible structure. Simulation model of the whole system, which is established by code written, is compared with the model established by finite element analysis software. Results are presented to show the efficiency of the vibration absorber, and then the effect of damping of the dynamic vibration absorber on vibration absorption is studied.