Recent studies have shown that many real networks follow the power-law distribution of node degrees. Instead of random connectivity, however, power-law connectivity suffers from the vulnerability of targeted attacks, since its interconnection is heavily relying on a very few nodes. In addition, the connectivity of power-law networks becomes more concentrated on the small group of nodes as time goes by, which can be explained by Barabasi and Albert?s rich-get-richer model. The rich-get-richer model is known as the most widely accepted generative model and follows the rule of preferential attachment to high-degree nodes. Thus, the preference of high-degree nodes to connect a newly created node renders the network less resilient as evolves. In this paper, we propose three different evolving strategies which can be applicable to the Internet topologies and the resiliency of evolving networks are measured by two resiliency metrics. From the experiments, we show that choosing an appropriate evolving strategy is more effective to increase the resiliency of network topology, rather than simply adding more links. Also, we show the possibility of improving the attack resiliency of Internet topology by adapting only a part of networks, e.g. 20- 40%, to a new evolving strategy, such as change from the maxdegree preference to the average-degree preference, which can be considered as a practical range of deployment.