In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of second-order evolution differential inclusions in Hilbert spaces. We use Bohnenblust–Karlin’s fixed point theorem to prove our main results. Further, we extend the result to study the approximate controllability concept with nonlocal conditions and also extend the result to study the approximate controllability for impulsive control systems with nonlocal conditions. An example is also given to illustrate our main results. © 2016, Springer International Publishing.