A new method for model reduction of linear discrete systems is proposed. It is based on the weighted impulse response gramians proposed here for discrete systems. These gramians are extensions of the ones proposed for linear continuous systems (Agathoklis and Sreeram 1988 a, 1990) and contain information on the input-output behaviour of the system. The reduced-order models are obtained by retaining the states corresponding to the dominant eigenvalues of these gramians and are stable if the original system is stable. The method is illustrated by a numerical example and is compared with well-known model reduction techniques