The passive control problem for a class of nonlinear singular discrete systems was analyzed. By the means of generalized Lyapunov function and linear matrix inequality, a sufficient condition was presented and a zero solution of nonlinear singular discrete system is asymptotically stable and passive. Based on the passive analysis, the condition was given for the existence of a state feedback passive controller, and it makes zero solution of the closed-loop system asymptotically stable and passive. Moreover, meamwhile the design method of the controller is given. An example was given to prove the validity of the results.