This paper studies the nonlinear restrictive mechanism of population growth by ana-lyzing the mathematical shape. Then a new mathematical model of population growth is putforward as follow:The model's analytic solution isAs the nonlinear density dependence index s<1, s= 1, s>1 and s→∞, the model correspondsto the Smith' s, the Logistic, the Cui-Lawson' s, and the Exponential models of populationgrowth, respectively. The paper also puts forward a method of parameter estimation of themodel which is called dir...