Animals possess the function of self-recovery for adapting the change in their living conditions. Can machinery, by bionic design, just like animals, also possess the function of self-recovery for making itself free of fault, or for eliminating fault automatically during operation? In this paper, a new theory of Engineering Self-recovery is discussed, which could provide theoretical basis and new methodology for creating a new generation of machinery with fault self-recovery function. The engineering self-recovery theory is different from engineering cybernetics. Engineering cybernetics endows machinery with purposive behavior which originally is one of animal’s common characteristics, while engineering self-recovery theory endows machinery with the new function of fault self-recovery which originally is another one of animal’s common characteristics. Under the guidance of engineering cybernetics, the automation of machinery has come true. While under the guidance of engineering self-recovery theory, a new generation of machinery with the new function of fault self-recovery could also be realized. The self-recovery system, which can provide fault self-recovery force to restrain fault force, is investigated in detail. Based on fault mechanism and risk analysis, and by bionic design, a fault self-recovery system, which is a dynamic system to store, supplement and transfer the self-recovery force, is endowed to a machine with the ability to maintain the machine in a health state. Also, the research in engineering application of the new concept, fault self-recovery, is on the way. As an example, the new concept centrifugal compressor with fault self-recovery function is discussed here with axial displacement and flow induced vibration fault self-recovery as examples to show the steps of fault self-recovery system construction such as fault mechanism, necessity, determination, possibility, fault tolerance, limitation and execution.