In response to multi-objective and multi-criteria performance evaluation problem for aero piston engine, the analytic hierarchy process (AHP) and entropy weight method (EWM) were used to transform it into single-objective and multi-level evaluation, and establish performance indicators, weight allocation, and evaluation systems under different operating conditions. Genetic algorithm-back propagation (GA-BP) neural network was employed to calculate and estimate its performance degradation state, the correctness of the performance evaluation system was verified by the joint simulation experiment. For the abnormal fuel injection holes leading to abnormal engine performance degradation as an example, this study explored the mechanism of its performance degradation from the perspective of combustion. The results showed that, when there were abnormal components of engine, the hierarchical entropy weight performance evaluation was a better method to reflect current performance status of the engine and make accurate judgments on its safety. The GA-BP computational model had a high accuracy, whose mean absolute percent error (MAPE) decreased by 3.5208%, 0.7027% and 3.7854%, respectively, compared with BP, radial basis function (RBF) and Elman models.