Based on the influences of network structure on wealth growths, for the character of wealth increasing and the
mechanism of wealth redistribution, a definition of an influence coefficient is given, and a network model of the wealth growth is proposed. System equations are used to obtain the time-varying equations of the total wealth, degree and cumulated wealth. Analysis results show that the influence coefficient can adjust the impacts of the node degree on the wealth growth, and has great effects on the network structure and cumulated wealth. Numerical simulations show that the influence coefficient can reduce Gini index and make the wealth distribution more even, and the cumulated wealth is linear with the node degree in a certain condition.