For the start-up process of the LOX/CH₄ expander cycle engine, containing unobserved events and unobserved states, the existing fault diagnosis methods are still not accurate enough, so we present a diagnosis method with partially observed Petri nets. Firstly, the system observation sequences are decomposed into elementary observation sequence of length 1 and linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence. Then, using the forward-backward algorithm extends the diagnosis range and using the parameter K limits the length of fault diagnosis sequence. Analyzing the unobserved transitions of the fire sequences, fired or not, so as to determine whether the faults are contained among the observed sequence. Finally, the LOX/CH₄ expander cycle engine start-up process is diagnosed by the fault diagnosis system of partially observed Petri nets. The experimental results show that the proposed algorithm can reduce the computational complexity as the original h_o^-1·e^h_o-K. It avoids the state space explosion problem because of the increasing of state space complexity. Meanwhile, it can be real-time tracking and online fault diagnosis which diagnosis accuracy can be reached 99.134%.