Investigation in this paper is a discrete Ablowitz-Ladik equation, which has certain applications in the electrical and optical systems. Based on the Hirota method, bilinear forms, dark one-and two-soliton solutions for such an equation are obtained. Soliton propagation and collision are graphically presented and analyzed: Dark one soliton is shown to maintain its original amplitude and width during the propagation, and discrete peaks of the propagating soliton are displayed. Overtaking collision between the two solitons with the different amplitudes is observed, and solitons have the same traveling direction with their amplitudes, velocities, and widths unchanged. A head-on collision between the two solitons is illustrated, and shapes of the two solitons keep invariant except for some phase shifts. Asymptotic analysis shows that the collision between the two solitons is elastic. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)