This paper deals with the stability of discrete time linear systems with time varying delays in state. In this paper, the magnitude of time-varying delays is assumed to be upper-bouded. The stability of discrete time linear systems with time-varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.