Abstract: The famous local-world model has presented a notion about local evolving, but the methodology it selected dose not conform to the reality very well. So, a modified version of the local-world evolving model is presented, with which the network generated possesses both the scale-free and small-world properties, and it's degree distribution represents a transition between power-law and exponential scaling. In contrast to the old model, it has a much bigger cluster coefficient which is in conformity with the real world, thus making the modified model more applicable than the old one.