Frequency response function (FRF) is a fundamental dynamic index, which is capable of reflecting structural dynamic properties using full-spectrum information. In spite of distinct merits over conventional modal parameters, the FRF has an observable drawback of multi-dimensionality, unsuited for damage characterization. Such a situation motivates an interesting subject, i.e., extracting low-dimensional, high-sensitivity damage index from the FRF. This study focuses on developing a valid damage index, called FRF change ratio, to detect extension of damage. An experiment towards cantilever beams is systemically conducted. The results show that the FRF change ratio can effectively reflects damage extension, and it is more sensitive than conventional natural frequencies. This new damage index holds promise for practical damage detection in beam-like structures.