This paper is concerned with the $H_{infty}$ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified $H_{infty}$ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for $H_{infty}$ state feedback controllers is given by solving a certain LMI. The design problem of optimal $H_{infty}$ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.