Growall-Bellman inequality is one of the most important inequalities investigating the qualitative and quantitative properties of solutions for differential equations such as stability, boundedness, asymptotic property. In this paper, some new generalized retarded nonlinear integral inequalities are discussed, and upper bound estimations of unknown functions are given by applying analysis technique and classical inequalities theories. These estimations can be employed ied to the certain nonlinear differential-integral equations. Finally, the upper bound of all solutions is given, which is the theoretic\, basis for the estimation of solutions, dynamical systems and control system.