Abstract: Due to the local-world evolving network over-simplifies the real network，a fitness local-world deleting evolving network model is raised，which considers the effects of adding nodes fitness and deleting nodes and edges.The research suggests that the choices of the new nodes do not only relate to the degrees of the existed nodes when adding fitness.Whatever deleting nodes or edges can increase the percent of the nodes whose degrees equal to 1 or 2，increase the average path length and decease the clustering coefficient.kmax and the clustering coefficient augment as the local world increases.Hence，expanding local-world can compensate the infection of the deleting.