In this paper, the stability analysis and controller design of a 2-D switched system with random disturbances are studied. First, based on the Fornasini-Marchesini local state-space model, a random discrete 2-D switched system model is proposed. Secondly, based on the method of switching quadratic Lyapunov function, Schur complement and linear matrix inequality the criterion of the sufficiency of the asymptotical stability under any switching signal is established. The extended average residence time method is used to obtain a sufficient criterion of the mean square exponential stability of the random discrete two-dimensional switching system under restricted switching conditions. According to the stability analysis results, the conditions for the existence of the state feedback controller are given and the corresponding state feedback controller is designed. Finally, two examples are given to illustrate the effectiveness of the proposed method.