This article is mainly concerned with the study of controllability for a class of second order control problems in Hilbert spaces, for which the uniqueness is not available.We show the approximate controllability of the non-linear problem via that of its corresponding linear problem by using the fixed point theory for multivalued maps with non-convex values.We also obtain some results on the continuity of solution map and the topological structure of the solution set of the problem at hand. Finally, an example is given for the demonstration of the theory obtained. © The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.