Growth and preferential attachment are the two ingredients of the scale-free network. Based on the Barabási-Albert scale-free model, we construct a more general model by replacing the linear preferential attachment with the nonlinear preferential attachment. We introduce different networks by controlling a parameter ? which decides the preferential attachment of our model. We try to find the influence of ? on the network structure and property. To study the influence, we investigate our model in three directions: topological characteristics, correlation of topological measures and attack vulnerability.