In order to explore further the mechanism responsible for scale-free networks, we introduce two extended models of the BA model. The model A, where the system incorporates the addition of new links between existing nodes, a new node with new links and the rewiring of some links at every time step, all sites are born with some initial attractiveness. We calculate analytically the degree distribution. The system self-organizes into a scale-free network, the scaling exponent γ>2. The model B is a new model; we consider that some old links are deleted with the anti-preferential probability. The result indicates that the system evolves itself into a scale-free network, the scaling exponent γ varies from 2 to 3.