A vibration absorber is used to reduce vibration of an Euler-Bernoulli beam with elastic supports subjected to a moving oscillator. Dynamic response of the beam under moving harmonic exciter with different moving velocities and different parameters are obtained. The critical velocity of the moving oscillator is determined and absorber parameters are optimized by numerical algorithm and effect of mass and damping on the absorber performance is investigated. When absorber is applied to the beam, effect of crack occurrence on its performance is investigated. Crack is assumed to be open and is modeled by sectional flexibility increase. Two different cases considered for crack severity. In each case, optimal absorber for intact beam is applied and dynamic response of the midpoint of the beam with different velocities of moving exciter is obtained. Results show although crack can increase dynamic deflection of the beam with absorber, dynamic deflection of cracked beam without considering absorber is higher than dynamic deflection of cracked beam with absorber used. It is found that the vibration absorber designed for intact beam keeps its performance in dynamic deflection reduction after crack occurrence and changing in structural dynamic.