Under investigation in this paper is a discrete integrable Ablowitz-Ladik equation, which has certain applications in the electrical and optical systems. Via the Hirota method and symbolic computation, the bilinear forms and N-bright soliton solutions are obtained. Propagation and interaction behaviors of the discrete solitons are analyzed through the one- and two-soliton solutions. The discreteness effects on soliton and soliton interaction are discussed. Asymptotic analysis shows that the interactions between two solitons are elastic. Head-on and overtaking interactions can be obtained with the choices of the directions of the velocities. Two kinds of overtaking interactions are investigated analytically and graphically, respectively. (C) 2014 Elsevier Ltd. All rights reserved.