Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies |f(t,x)|≤μe-ε|t|. However, this condition is very restricted. There are few functions satisfying |f(t,x)|≤μe-ε|t|. In some sense, this assumption is not reasonable enough. More suitable assumption should be |f(t,x)|≤μ. To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption |f(t,x)|≤μ. In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper. © 2014 Yong-Hui Xia et al.