The on-board sensor fault detection and isolation (FDI) system is essential to guarantee the reliability and safety of an aero engine. In this paper, a novel online sequential extreme learning machine with memory principle (MOS-ELM) is proposed for detecting, isolating, and reconstructing the fault sensor signal of aero engines. In many practical online applications, the sequentially coming data chunk usually possesses a characteristic of timeliness, and the overdue training data may mislead the subsequent learning process. The proposed MOS-ELM can improve the training process by introducing the concept of memory principle into the online sequential extreme learning machine (OS-ELM) to tackle the timeliness of the data chunk. Simulations on some time series problems and some benchmark databases show that MOS-ELM performs better in generalization performance, stability, and prediction accuracy than OS-ELM. The experiment results of the MOS-ELM-based sensor fault diagnosis system also verify the excellent generalization performance of MOS-ELM and indicate the effectiveness and feasibility of the developed diagnosis system.