A robust fault diagnosis approach for aero-engine compressor sensor based on the linear matrix inequality(LMI) and the H∞ optimization theory was presented for aero-engine compressor health monitoring. The aero-engine compressor discrete model was obtained by using the linear fitting approach based on the neural network in consideration of both the uncertainties of model and noise. The design parameters of unknown input observer (UIO) were obtained by solving LMI and H∞ optimization for fault diagnosis of sensor with strong robustness. The main advantage of this approach lies in that it can handle both uncertainties of model and noise simultaneously compared with fault diagnosis approach of UIO existing. The numerical simulation was conducted by using the gas turbine compressor model provided by ALSTOM Company. The result shows that less than 2% sensor fault can be detected under white noise modeling uncertainty and sinusoidal external disturbance.