Abstract: Researchers have been constructing damage indicators with modal parameters to identify structural damage for a long time, and quite a few such indicators have been put forward. However, it is hard to find an indicator capable of detecting damage accurately under the effect of noise which is always associated with the modal parameters extracted from recorded signals. Based on improved damage variable indicator and elemental stiffness reduction factor (ESRF), utilizing the practical complete modal space theory, the authors propose a two-stage damage identification scheme. In the first step, the proposed scheme localizes damage by improved damage variable indicator. And then, a complete modal space is constructed with only a few lower modes, which is used to quantify damage with the improved ESRF. A few simulations including a continuous beam, a simple supported truss and a frame with different damage scenarios are selected as case study to compare the performance of the ESRF and the proposed scheme. The results show that the suggested scheme is better than the ESRF when only a few lower modes are utilized, and it can both localize and quantify damage at a certain noise level.