An optimal regression approach to fault diagnosis of liquid rocket engine is presented in this paper，which can diagnose a number of faults with fewer measurements. When the kinds of fault are fewer and the faults are not serious，rather satisfactory results of fault isolation and fault severity estimation are obtained. When the kinds of fault are fewer and the faults are serious，this approach still gives rather good fault isolation result. When there exist several kinds of fault and the faults are serious，the diagnostic effect decreases somewhat. This indicates that the result of this method is satisfactory at a wide value range of fault factors.