In this paper, we mainly discuss finite horizon $H_{2}/H_{\infty}$ control for discrete-time time-delay systems with infinite Markov jumps. Firstly, we present a stochastic bounded real lemma, which is crucial to solve mixed $H_{2}/H_{\infty}$ control problem of the considered systems. With the variable substituting method, we transform a discrete system with control delay into a standard non-delay system. Then a sufficient and necessary condition is presented for the $H_{2}/H_{\infty}$ control problem of infinite Markov jump systems.