Crack damage brings a serious threat to the safety of mechanical and civil structures, and the problem of incipient damage identification of structures has been paying attention as a puzzle by many researchers in recent years. To seek for an alternative solution of the problem, a method for incipient crack localization using the slope of the anti-resonance curve is proposed in this paper. The method makes use of the driving-point mechanical impedance characteristics of cracked beams stimulated by harmonic force. To characterize the local discontinuity due to the presence of crack, a simplified rotational spring model is presented to model the crack. Subsequently, the proposed method is verified by a numerical example of cracked beam under simple support or cantilever boundary conditions.