Abstract: The definition of strictly passive is proposed for discrete-time singular systems and the passive control problem is discussed under bounded energy exogenous inputs. By means of linear matrix inequalities and generalized algebra Riccati inequalities, a sufficient condition is derived as such that a prescribed discrete-time singular system is admissible and strictly passive. Moreover, a sufficient condition is provided for the existence of a static state feedback controller such that the resulting closed-loop system is both admissible and strictly passive. The design method for such state feedback controller is also given. An example was carried out to prove the sufficient conditions.