This paper provides a method to design a robust observer for matrix-Lipchitz nonlinear systems with measurement delay. The design procedure will produce a stable observer when only the measurement delay is present. The design procedure achieves a L 2 performance in the presence of model uncertainties, unknown disturbance input, and measurement noise. The conditions for the existence of the said observers are formulated as Linear Matrix Inequalities (LMIs) that can be solved offline using commercial solvers. Compared to previous literature, the proposed conditions are both necessary and sufficient. The observer design procedure is demonstrated through two illustrative examples.