Based on the feature of WWW networks,a Poisson NPA competition model with dependent attractiveness of nodes is proposed.The model is gene ralized with initial attractiveness.The stationary average degree distribution of the model is calculatedand it is proved that the network is scale-free by using Poisson theory.The relation between the coefficient A of asymptotically linear attractiveness and the number m of edges of a new node is acqaired.Theoretical analysis and simulation show that the power-law exponent of the model is in interval(2,m 1),and the smaller the |A|/m the less the error between the theoretical and simulated results.