In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which the undelayed part admits an evolution operator. We discuss the problems by utilizing theory of evolution operators, Schauder fixed point theorem and Banach fixed point theorem. Some new results on existence and uniqueness of solutions of the considered equation are obtained on the infinite internal [0, +∞). In the end, the obtained results are applied to a class of non-autonomous heat equations with state-dependent nonlocal conditions.