Frequent convergence of the solution of a nonlinear discrete dynamic system x_（n＋1）=3/4- x_n~2 is discussed by using definitions and properties of frequency measure of real sequences. Through discussing the monotonicity and boundedness of subsequences of the solution

we proved that if the initial value x_0∈（-1/2

1/2）

then the solution X = {x_n}_（n = 0）~∞ of the difference equation has one frequent limit 1/2; if x_0∈（-∞

-3/2）∪（3/2

＋∞）

then the solution X = {x_n}_（n = 0）~∞ of the difference equation is frequently inside （-∞

-3/2）.