This paper studies and predicts the number growth of China’s mobile users by using the power-law regression.We find that the number growth of the mobile users follows a power law.Motivated by the data on the evolution of the mobile users,we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model,in which the nodes grow following a power-law acceleration.The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process.This result shows that the model generates appropriate power-law connectivity distributions.Therefore,we find a power-law acceleration invariance of the scale-free networks.The numerical simulations of the models agree with the analytical results well. This paper studies and predicts the number growth of China’s mobile users by using the power-law regression. We found that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, where the nodes grow following a power-law acceleration. expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process .This result shows that the model generates appropriate power-law connectivity distributions.Therefore, we find a power-law acceleration invariance of the scale-free networks. Numerical simulations of the models agree with the analytical results well.