In this paper, controllability and near-controllability of discrete-time inhomogeneous bilinear systems without drift are studied. Necessary and sufficient conditions for controllability and near-controllability of the systems are respectively presented. In particular, algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided. Examples are shown to demonstrate the conceptions and results of the paper. (C) 2014 Elsevier Ltd. All rights reserved.