After some damaging blackouts, voltage stability and collapse have become worldwide concerned problems. In this paper, we focus on the aspect of voltage stability. An improved voltage stability index named LI is presented, which can give an accurate indication to power system voltage instability with considering the influence of the load model. Its calculating speed is very fast, so it can be used in the on-line monitoring and control of power system voltage stability. An appropriate external equivalent method is also presented to speed-up the calculation. So index-LI can be used in regional operating centers of the interconnection power systems. As an application of index-LI, approaches to identify voltage stability weak buses, coherent generator set and coherent load set of a weak bus are given in the end. New-England system and IEEE 50-generator-145-bus system are used to illustrate the accurateness and effectiveness of our methods.