Monitoring the aircraft engine fuel flow is critical to the flight safety and the aircraft maintenance economy. Aim at predicting the aircraft engine fuel flow accurately and quickly, an aircraft engine fuel flow prediction method based on the process neural network is proposed in this paper. The learning speed of the existing learning algorithms (e.g. BP learning algorithm) for process neural network is too slow for the practical application. A Levenberg-Marquardt learning algorithm based on the expansion of the orthogonal basis functions is developed to raise the adaptability of the process neural network to the real problems. Finally, the proposed prediction method with the corresponding learning algorithm is utilized to predict the fuel flow of some aircraft engine, the results indicate that the proposed prediction method seems to perform well and appears suitable for using as an aircraft engine health condition monitoring tool, and the comparative results also indicate that the Levenberg-Marquardt learning algorithm has a faster learning convergence speed and a higher prediction accuracy than the BP learning algorithm.