In this paper, a mathematical model is set up to inquire population change under interaction between the economic growth and human population carrying capacity. By introducing the population growth equation with variable carrying capacity into the classical Solow model and combining the population growth equation, we obtain a two-dimensional dynamical system. It is proved that the dynamical system has a unique equilibrium and the solution of the dynamical system is asymptotically stable. By qualitative analysis, we obtain that the population growth rate increases from zero to a positive level firstly and then decreases to zero and per capita capital increases strictly along a normal economic growth path. Therefore, the model implies that the demographic transition appears under the interaction between economic growth and human population carrying capacity.
