In this paper, the problem of ellipsoidal set-membership estimation of systems with quantized measurement output is studied. The output is quantized by a logarithmic quantizer. With the sector bound property of the logarithmic quantizer, the quantized problem is converted into a robust control problem. An ellipsoidal set-membership filter with two parameters to be designed is used to estimate the system state. The estimation is obtained by solving the linear matrix inequality optimization problem. Some special cases of the estimation problem are analyzed in detail. A simulation example is given to show the effectiveness of the proposed results in the end.