Abstract: A new model of world population growth, including discrete equations for the dynamics of percentage increases in integral inflows and outflows and a balance equation for the population size, is proposed. The principle of dynamic balance of a demographic process and the condition of interval dynamic consistency based on this principle are formulated. A sample example of forecasting world population growth in the period from 2011 to 2021 is given, which demonstrates the possibility of building linear dynamic trends in the percentage growth of the integral number of dead people dynamically consistent with corresponding intervals of statistics on the integral numbers of children born in earlier periods. Based on the proposed model, world population growth after 2021 is predicted assuming that the population size will reach 9.466 billion in 2050 and will attain the maximum level of 9.651 billion in 2062, after which the world population will decline to amount to 8.670 billion in 2100.