This paper is concerned with the problem of robust filtering for uncertain 2-D discrete systems in Fornasini-Marchesini second local state-space model with state-varying delays. The parameter uncertainty is assumed to be norm-bounded. A 2-D stable filter is designed to ensure that a prescribed $H{infty}$ performance level is fulfilled for all admissible uncertainties. A linear matrix inequality (LMI) approach is developed to solve the above problem, and delay-dependent conditions for the solvability are obtained. A illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.