In order to solve the drawback that traditional algorithms cannot indicate the crucial load buses in the specific area, a novel method is proposed to partition a group of load buses and to indicate the crucial load buses based on local voltage stability index. According to the physical significance of local voltage stability index, this method initially maps the load buses of a specific power system into the multivariate load space where the space distance is defined as the electrical distance between load buses. In the following stage, the load subgraph model is established as the equivalence of load space, then the spectrum clustering algorithm is utilized to indicate the reasonable partition for a group of load buses recursively. Subsequently, the given partition is supposed to be synthesized with local voltage stability sensitivity matrix and consequently obtain the crucial load bus in each zone. The IEEE 14-bus and IEEE 118-bus test cases are used to numerically validate the feasibility and effectiveness of the proposed method.