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Baseed on the discussion about the existence and design method of full-order observer for systems with monotone nonlinearities, a reduced-order observer design method is developed under the assumption that a linear matrix inequality (LMI)has positive definite matrix solution and the reduced-order observer gain matrix is computed by the solution of LMI. By a linear transformation, a reduced-order observer which does not contain the information of the derivative of the system output is provided.A model is simulated and some conclusions are drawn based on the comparison of the results of reduced-order observer to that of full-order observer. The simulation shows that the design method developed by this paper has good performance.