Leslie's matrix calculation model is fit for investigating the size of population Nt at a series of discrete times t = 0,1,2, ... This paper dealt with some properties of this model. We studied the dynamic behavoir of variation of Nt, the condition to decrease Nt and the influence of the pre-birth age, -when artificial measures were taken for control. Correspondingly, We derived several approximate formulas. We made a case study and carried out calulations. The results have shown that these formulas are rat...