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There are many observer design approaches that have been developed to estimate the state of a linear time delay system. This paper focuses on the observer design problem for two-dimensional (2-D) continuous systems with delays proposed by Roesser’s state space model. A new sufficient condition for 2-D state observer design of 2-D continuous-time systems with delays is developed. The key point is that the Lyapunov theory that is used here allows us to solve the problem using the technique of linear matrix inequalities, which is used to establish the 2-D state observers with delays. Finally, to illustrate the effectiveness of the proposed methodology, a numerical example is provided.